One Model To Rule Them All
Alex Kale
9/24/2018
Experiment 2
Load Raw Data
These data were collected in a two-alternative forced choice experiement where participants judged stimuli at varying levels of evidence and were either correct or incorrect on each trial. In experiment 2, each participant was assigned to one of three possible uncertainty visualization conditions: regular HOPs, fast HOPs, or line ensembles.
# e1df = read.csv("E1-AnonymousRawData-InferenceSample.csv")
e2df = read.csv("E2-AnonymousRawData.csv")Preprocessing
Reformat the raw data from the experiment as a list, changing types to integers as needed and taking the absolute value of ratio (i.e., stimulus intensity). This step will enable Stan to correctly process the data.
# prepare data for model
useData <-data_frame(
"correct" = as.integer(e2df$Correct),
"intensity" = abs(e2df$Ratio),
"condition" = as.factor(e2df$Visualization),
"subject" = as.factor(as.integer(as.factor(e2df$WorkerID)))
)Model Specification
Our statistical model is a variation on Bayesian hierarchical probit regression.
We model the probability of a correct response from 0.5 (guessing) to 1 - lapse rate (the maximum estimated performance for each participant) as a function of stimulus intensity using a scaled and shifted cumulative normal distribution. This is called the psychometric function, and it will be used as the inverse link function in our regression model. Here are the parameters of the psychometric function:
- threshold: mean of the cumulative Gaussian in stimulus intensity units,
- spread: standard deviation (sd) of the cumulative Gaussian in stimulus intensity units,
- guess rate: the lower bound of the cumulative probability density which is .5 for a two alternative forced choice task with equally likely alternatives
- lapse rate: the rate of error for an individual due to lapses of attention which are independent of the stimulus
We define the psychometric function in R so that we can use it in postprocessing.
psychometric <- function(intensity,m,sd,guess,lapse){
# handle arguments
if(missing(guess)) {
guess <- .5
}
if( missing(lapse)) {
lapse <- 0
}
intensity <- as.matrix(intensity)
# set upper and lower bounds
lowerBound <- guess
upperBound <- 1 - lapse
# calculate z score for each level of intensity
r <- dim(intensity)[1]
c <- dim(intensity)[2]
z <- (intensity - m * matrix(1, r, c)) / sd
# scale cumulative probability density between upper and lower bound
p <- lowerBound + pnorm(z / sqrt(2)) * (upperBound - lowerBound)
return(p)
}Below is the specification of the statistical model. Note the following features of the model:
- We are modelling correctness as a binomial distributed outcome with the probability of being correct as a transformed linear model of ratio and visualization condition.
- We use a scaled and shifted probit (the inverse of the psychometric function) as the link function for our linear model.
- The threshold, spread, and lapse rate parameters of the model are estimated for each subject while guess rate is assumed to be .5 based on the design of the experiment.
- We estimate the effect of each visualization condition via dummy coding.
The point of this exercise is that all parameters, both at the subject level (psychometric function parameters) and the group level (effects of visualization condition), are all estimated from raw data within one unified model.
# model specification in Stan
stanCode <-
'data {
int<lower=0> N; // number of obs
int<lower=0> N_subject; // number of subjects
int<lower=0> N_condition; // number of visualization conditions
int<lower=0,upper=1> correct[N]; // correctness of judgments on each trial
real<lower=0> intensity[N]; // stimulus intensity on each trial
int<lower=0> subject[N]; //subject index for each observation
int<lower=1,upper=N_condition> condition[N_subject]; // visualization condition for each subject
}
parameters {
// hyperparameters for sigma of threshold, spread, and lapse
real<lower=0> sigma_log_threshold;
real<lower=0> sigma_log_spread;
real<lower=0> sigma_logit_lapse;
// effects of visualization conditions (transformed means per condition for threshold, spread, and lapse)
vector[N_condition] b_threshold;
vector[N_condition] b_spread;
vector[N_condition] b_lapse;
// for non-centered parameterization
vector[N_subject] threshold_zoffset;
vector[N_subject] spread_zoffset;
vector[N_subject] lapse_zoffset;
}
transformed parameters {
// non-centered parameterization of threshold, spread, and lapse parameters of the PF for each subject
vector<lower=0>[N_subject] threshold;
vector<lower=0>[N_subject] spread;
vector<lower=0,upper=1>[N_subject] lapse;
threshold = exp(b_threshold[condition] + threshold_zoffset*sigma_log_threshold);
spread = exp(b_spread[condition] + spread_zoffset*sigma_log_spread);
lapse = inv_logit(b_lapse[condition] + lapse_zoffset*sigma_logit_lapse);
}
model {
vector[N] p; // probability of being correct on each trial
threshold_zoffset ~ normal(0,1); // priors for offsets per subject for non-centered parameterization of PF
spread_zoffset ~ normal(0,1);
lapse_zoffset ~ normal(0,1);
sigma_log_threshold ~ cauchy(0,1); // priors for hyperparameters
sigma_log_spread ~ cauchy(0,1);
sigma_logit_lapse ~ gamma(2,2);
b_threshold ~ normal(0,2); // priors for visualization effects
b_spread ~ normal(0,2);
b_lapse ~ normal(log(0.05/(1 - 0.05)),fabs(log(0.196/(1 - 0.196)))); // centered on logit(0.05)
// sigma_logit_lapse ~ exponential(3);
for (i in 1:N) {
// psychometric function as inverse link function
p[i] = (0.5 - lapse[subject[i]])*Phi((intensity[i] - threshold[subject[i]])/spread[subject[i]]/sqrt(2.0)) + 0.5;
}
correct ~ binomial(1,p);
}'
# convert to model
mdlSpec <- stan_model(model_code = stanCode)## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:14:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Dense:1:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Core:531:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:14:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Dense:2:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/LU:47:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:14:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Dense:3:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Cholesky:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Jacobi:29:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:14:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Dense:3:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Cholesky:43:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:14:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Dense:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/QR:17:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Householder:27:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:14:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Dense:5:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/SVD:48:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:14:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Dense:6:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Geometry:58:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:14:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core/matrix_vari.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat/fun/Eigen_NumTraits.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Dense:7:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Eigenvalues:58:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:96:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/csr_extract_u.hpp:6:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Sparse:26:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/SparseCore:66:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:96:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/csr_extract_u.hpp:6:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Sparse:27:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/OrderingMethods:71:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:96:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/csr_extract_u.hpp:6:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Sparse:29:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/SparseCholesky:43:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:96:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/csr_extract_u.hpp:6:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Sparse:32:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/SparseQR:35:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:96:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/csr_extract_u.hpp:6:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/Sparse:33:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/IterativeLinearSolvers:46:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/RcppEigen/include/Eigen/src/Core/util/ReenableStupidWarnings.h:10:30: warning: pragma diagnostic pop could not pop, no matching push [-Wunknown-pragmas]
## #pragma clang diagnostic pop
## ^
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core.hpp:44:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/core/set_zero_all_adjoints.hpp:14:13: warning: unused function 'set_zero_all_adjoints' [-Wunused-function]
## static void set_zero_all_adjoints() {
## ^
## In file included from file1332867e32ce6.cpp:8:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/src/stan/model/model_header.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math.hpp:4:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/rev/mat.hpp:12:
## In file included from /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat.hpp:70:
## /Library/Frameworks/R.framework/Versions/3.5/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/autocorrelation.hpp:18:8: warning: function 'fft_next_good_size' is not needed and will not be emitted [-Wunneeded-internal-declaration]
## size_t fft_next_good_size(size_t N) {
## ^
## 15 warnings generated.Next we fit the model to our data using Stan.
# run model (actually load it instead of running)
# mdl = sampling(
# mdlSpec,
# data = compose_data(useData,condition = x_at_y(condition, subject),.n_name = n_prefix("N")),
# chains = 2,
# cores = 2,
# warmup = 1000,
# iter = 2000,
# control = list(adapt_delta=0.99,max_treedepth = 15)
# )We save the run of the model and load it, so that we don’t have to run it every time.
# saveRDS(mdl,'oneMdl.rds')
mdl <- readRDS('oneMdl.rds')Check Model Perfomance
This kind of Bayesian model samples from a Markov Chain Monte Claro algoritm to estimate each parameter in our model. Here we can see whether the four separate simulations we ran above converged (a sign of reliable estimates) and whether the any the samples from any simulation contain autocorrelation (a sign that out simulation got stuck at a given location in parameter space, and we should run the model fit again and possibly change our model specification or priors). We check this by looking at a traceplot.
traceplot(mdl,pars=c('b_threshold[1]','b_spread[1]','b_lapse[1]','b_threshold[2]','b_spread[2]','b_lapse[2]','b_threshold[3]','b_spread[3]','b_lapse[3]','sigma_log_threshold','sigma_log_spread','sigma_logit_lapse','threshold[1]','spread[1]','lapse[1]'))
Here, we just want to see that the simulation is not getting stuck on particular parameter values.
Let’s also check whether our model had any problems identifying any of our parameters due to highly correltated parameter values. We check this using a pairs plot.
pairs(mdl,pars=c('b_threshold[1]','b_spread[1]','b_lapse[1]','b_threshold[2]','b_spread[2]','b_lapse[2]','b_threshold[3]','b_spread[3]','b_lapse[3]','sigma_log_threshold','sigma_log_spread','sigma_logit_lapse','threshold[1]','spread[1]','lapse[1]'))
Too much correlation between posterior samples would here would indicate that our model fit is probably not properly estimating these parameters due to non-identifiability.
Let’s look at the summary, paying special attention to the Rhat which should be very close to 1, and n_eff which should be within two orders of magnitude of the number of non-warmup iterations.
# get and print model summary
mdlSummary <- summary(mdl)
print(mdlSummary$summary)## mean se_mean sd
## sigma_log_threshold 1.083179e-01 0.0040759773 0.052589661
## sigma_log_spread 2.596112e-01 0.0043354470 0.059472580
## sigma_logit_lapse 1.974326e+00 0.0104474067 0.241475978
## b_threshold[1] 9.381986e-01 0.0012303056 0.051394479
## b_threshold[2] 8.672131e-01 0.0011278735 0.052430262
## b_threshold[3] 8.558368e-01 0.0014261445 0.062863069
## b_spread[1] 4.432826e-01 0.0022099637 0.080406625
## b_spread[2] 4.754875e-01 0.0038033414 0.085631759
## b_spread[3] 5.998302e-01 0.0037291347 0.093357858
## b_lapse[1] -4.629199e+00 0.0181275600 0.446993037
## b_lapse[2] -4.788735e+00 0.0235938334 0.475306032
## b_lapse[3] -4.341325e+00 0.0211640281 0.465242575
## threshold_zoffset[1] 1.291453e-01 0.0166141443 0.998176373
## threshold_zoffset[2] 1.387799e-01 0.0162620915 0.936986437
## threshold_zoffset[3] -1.069167e-01 0.0153426116 0.903451243
## threshold_zoffset[4] 5.297911e-02 0.0168539030 0.907713589
## threshold_zoffset[5] -2.326056e-03 0.0175076291 0.968626186
## threshold_zoffset[6] -3.920160e-01 0.0199157153 0.873154005
## threshold_zoffset[7] 2.311405e-01 0.0175374790 0.971636855
## threshold_zoffset[8] -1.470438e-01 0.0182446186 0.951839170
## threshold_zoffset[9] -4.282742e-01 0.0223752339 0.849749907
## threshold_zoffset[10] -5.848093e-03 0.0174487255 0.978475839
## threshold_zoffset[11] 1.557685e-03 0.0174288598 0.926253353
## threshold_zoffset[12] 1.169680e-02 0.0161286940 0.921028488
## threshold_zoffset[13] -5.651016e-02 0.0161334063 0.935462213
## threshold_zoffset[14] -9.145528e-02 0.0170726568 0.971051074
## threshold_zoffset[15] 3.818051e-01 0.0176941840 0.985044850
## threshold_zoffset[16] -2.721953e-01 0.0174532450 0.920676942
## threshold_zoffset[17] -2.003886e-01 0.0166331531 0.895264290
## threshold_zoffset[18] -5.395294e-01 0.0224147746 0.925240509
## threshold_zoffset[19] 1.211668e-02 0.0176874760 1.010957377
## threshold_zoffset[20] -5.078965e-03 0.0159519596 0.958858403
## threshold_zoffset[21] 1.280231e-01 0.0180762827 0.959638715
## threshold_zoffset[22] -2.024857e-01 0.0172630944 0.923877327
## threshold_zoffset[23] 3.058202e-01 0.0214975398 0.955882467
## threshold_zoffset[24] -1.947190e-02 0.0168797657 0.986154278
## threshold_zoffset[25] 4.534405e-01 0.0228202200 1.053576182
## threshold_zoffset[26] 1.596064e-01 0.0193159601 1.009058339
## threshold_zoffset[27] 1.488109e-01 0.0149034595 0.914742398
## threshold_zoffset[28] 2.505733e-01 0.0200584645 0.989407472
## threshold_zoffset[29] 5.768787e-01 0.0243527455 0.991640337
## threshold_zoffset[30] 2.617813e-01 0.0195367538 1.030414155
## threshold_zoffset[31] -2.080289e-01 0.0186739445 0.929657097
## threshold_zoffset[32] 1.488973e-01 0.0199065754 1.025198648
## threshold_zoffset[33] -3.594494e-01 0.0196091669 0.940970564
## threshold_zoffset[34] -5.251153e-02 0.0172756408 0.917320965
## threshold_zoffset[35] 1.259826e-01 0.0189249368 0.916447330
## threshold_zoffset[36] -3.969212e-01 0.0196144838 0.931763429
## threshold_zoffset[37] 9.612675e-02 0.0205345758 1.017949766
## threshold_zoffset[38] 1.946599e-01 0.0172914479 0.941088363
## threshold_zoffset[39] -4.374537e-01 0.0193163740 0.941993087
## threshold_zoffset[40] -5.424103e-01 0.0205878509 0.882940331
## threshold_zoffset[41] 2.324385e-02 0.0187387146 0.908564882
## threshold_zoffset[42] 1.445721e-01 0.0171240808 0.969906509
## threshold_zoffset[43] 2.052500e-01 0.0179137176 0.956998322
## threshold_zoffset[44] -2.781470e-01 0.0163785219 0.881479215
## threshold_zoffset[45] -1.072034e-01 0.0172506921 0.947960280
## threshold_zoffset[46] -1.331618e-02 0.0166041721 0.969627041
## threshold_zoffset[47] -5.979871e-01 0.0236927946 0.957991260
## threshold_zoffset[48] -5.731168e-01 0.0196683095 0.919344435
## threshold_zoffset[49] -5.916742e-01 0.0201234871 0.884104824
## threshold_zoffset[50] 1.469255e-01 0.0198306363 1.049715455
## threshold_zoffset[51] 5.221296e-03 0.0196877843 0.991757422
## threshold_zoffset[52] 2.632039e-01 0.0183990522 1.005245882
## threshold_zoffset[53] -4.605234e-01 0.0239848480 0.902870357
## threshold_zoffset[54] 2.493949e-01 0.0168321136 0.914593485
## threshold_zoffset[55] 3.097309e-01 0.0220074649 0.926089253
## threshold_zoffset[56] -3.463109e-01 0.0198429975 0.910618470
## threshold_zoffset[57] -4.853517e-01 0.0190496191 0.912321775
## threshold_zoffset[58] 2.326163e-01 0.0175078673 0.889921216
## threshold_zoffset[59] 5.148747e-01 0.0243106153 1.028177063
## threshold_zoffset[60] 3.430222e-01 0.0168320199 0.953004716
## threshold_zoffset[61] 3.732068e-01 0.0200248789 1.000371419
## threshold_zoffset[62] -7.270605e-02 0.0173399920 0.951556639
## threshold_zoffset[63] 1.883492e-01 0.0175646672 0.974644898
## threshold_zoffset[64] 3.514790e-01 0.0199251700 0.957852008
## threshold_zoffset[65] -2.486205e-01 0.0170581175 0.911338543
## threshold_zoffset[66] 5.169429e-01 0.0221617000 1.017798435
## threshold_zoffset[67] -4.305144e-01 0.0207031443 0.907726703
## threshold_zoffset[68] 2.484263e-01 0.0203847587 0.996909105
## threshold_zoffset[69] -4.087539e-01 0.0195388191 0.896722983
## threshold_zoffset[70] -5.609487e-01 0.0210925021 0.916384709
## threshold_zoffset[71] 3.293143e-02 0.0164641036 0.924953859
## threshold_zoffset[72] 2.271494e-01 0.0207279055 1.012072072
## threshold_zoffset[73] 9.763396e-02 0.0178797653 0.943331273
## threshold_zoffset[74] -1.128064e-01 0.0142583010 0.858376684
## threshold_zoffset[75] 1.761938e-01 0.0180963658 0.947889668
## threshold_zoffset[76] -7.008710e-02 0.0178648278 0.944119865
## threshold_zoffset[77] -8.630200e-01 0.0230310771 0.878226469
## threshold_zoffset[78] 9.942984e-02 0.0165208548 0.932787074
## threshold_zoffset[79] -5.339056e-01 0.0231417325 0.905536048
## threshold_zoffset[80] 2.712175e-01 0.0184201604 0.972626925
## threshold_zoffset[81] -3.247499e-01 0.0177505754 0.955810639
## threshold_zoffset[82] 2.779971e-01 0.0195294130 0.976787592
## threshold_zoffset[83] 2.290239e-01 0.0168638098 0.906490146
## threshold_zoffset[84] -1.365546e-01 0.0178787712 0.885025086
## threshold_zoffset[85] -4.226669e-01 0.0199981145 0.871870396
## threshold_zoffset[86] 4.311971e-02 0.0164427925 0.936429030
## threshold_zoffset[87] 1.454371e-01 0.0168066968 0.993745285
## threshold_zoffset[88] 2.033892e-01 0.0166047975 0.905666803
## threshold_zoffset[89] 2.410122e-01 0.0198546778 0.979725177
## threshold_zoffset[90] 4.751317e-01 0.0254214425 1.032186773
## threshold_zoffset[91] -4.954947e-01 0.0205652421 0.903213874
## threshold_zoffset[92] 2.776856e-01 0.0189708269 1.016657927
## threshold_zoffset[93] 3.254236e-02 0.0179003883 0.968812139
## threshold_zoffset[94] 3.522647e-02 0.0170484701 0.995930529
## threshold_zoffset[95] 6.246901e-02 0.0192621444 0.950904308
## threshold_zoffset[96] -1.493451e-01 0.0200777483 1.004890675
## threshold_zoffset[97] -1.286489e-01 0.0182440302 0.985254632
## threshold_zoffset[98] -5.395559e-01 0.0207032387 0.942006808
## threshold_zoffset[99] 2.561822e-01 0.0172500816 0.947609923
## threshold_zoffset[100] 9.974911e-02 0.0186291328 0.969476413
## threshold_zoffset[101] 5.990820e-02 0.0165920626 0.996633388
## threshold_zoffset[102] -2.163471e-01 0.0182270762 0.906309568
## threshold_zoffset[103] 4.217122e-02 0.0160533593 0.988391673
## threshold_zoffset[104] -2.519046e-01 0.0205779255 0.923268322
## threshold_zoffset[105] -6.426944e-02 0.0173653336 0.885961222
## threshold_zoffset[106] 1.920079e-01 0.0166953786 0.952407096
## threshold_zoffset[107] 1.176908e+00 0.0492978367 1.221676694
## threshold_zoffset[108] -1.542244e-01 0.0171404594 0.979143723
## threshold_zoffset[109] -7.933444e-02 0.0158388677 0.921838117
## threshold_zoffset[110] 2.121122e-01 0.0187204176 0.986134223
## threshold_zoffset[111] 1.095440e-01 0.0192051336 0.938480941
## threshold_zoffset[112] 7.443418e-02 0.0161070134 0.931180635
## threshold_zoffset[113] -3.206446e-01 0.0211207682 0.927606607
## threshold_zoffset[114] -9.196777e-02 0.0175991129 0.952065076
## threshold_zoffset[115] -2.695802e-01 0.0170795286 0.923035709
## threshold_zoffset[116] 1.810812e-02 0.0157725913 0.888855637
## threshold_zoffset[117] 2.767608e-01 0.0191553917 0.951615360
## threshold_zoffset[118] 8.321374e-02 0.0180343398 0.968773223
## threshold_zoffset[119] 3.510475e-01 0.0174752310 0.963811166
## threshold_zoffset[120] -3.142408e-02 0.0174926239 0.927741039
## threshold_zoffset[121] 5.705771e-02 0.0181373101 0.914108784
## threshold_zoffset[122] -7.171032e-02 0.0160945633 0.894552094
## threshold_zoffset[123] -3.532981e-02 0.0178381391 0.962140485
## threshold_zoffset[124] 3.240472e-01 0.0214484167 0.966640275
## threshold_zoffset[125] 3.189316e-01 0.0209343774 0.954294722
## threshold_zoffset[126] 2.350615e-01 0.0175893254 0.991142481
## threshold_zoffset[127] 3.948261e-01 0.0211599161 0.983469956
## threshold_zoffset[128] -1.018112e-01 0.0167415833 0.982564367
## threshold_zoffset[129] -5.063109e-01 0.0207361206 0.892295468
## threshold_zoffset[130] 2.716514e-01 0.0197809466 0.960524152
## threshold_zoffset[131] -4.856522e-02 0.0180888259 0.891726451
## threshold_zoffset[132] 2.258336e-01 0.0175366699 0.981796450
## threshold_zoffset[133] -1.270958e-01 0.0173744496 0.943833889
## threshold_zoffset[134] 2.935794e-01 0.0181741663 0.970417523
## threshold_zoffset[135] -9.195009e-03 0.0164024230 0.984743838
## threshold_zoffset[136] 2.985240e-01 0.0189595965 0.994957819
## threshold_zoffset[137] -1.348492e-01 0.0168748948 0.884372176
## threshold_zoffset[138] 2.256287e-01 0.0190779749 0.924883920
## threshold_zoffset[139] 4.610242e-01 0.0239978217 1.002161808
## threshold_zoffset[140] -1.369042e-01 0.0186248246 0.964755303
## threshold_zoffset[141] 3.833643e-02 0.0183821796 0.949566296
## threshold_zoffset[142] 1.976023e-01 0.0175754266 0.934709192
## threshold_zoffset[143] 1.636911e-01 0.0182836407 0.898568706
## threshold_zoffset[144] 1.780262e-01 0.0173511621 0.932766282
## threshold_zoffset[145] 2.171908e-02 0.0181189661 0.921511456
## threshold_zoffset[146] 2.756778e-01 0.0178203598 0.956295926
## threshold_zoffset[147] -9.555970e-01 0.0307562713 0.925581740
## threshold_zoffset[148] 7.811345e-02 0.0174022495 0.930734628
## threshold_zoffset[149] -4.109605e-01 0.0183309539 0.920024988
## threshold_zoffset[150] -1.390998e-01 0.0162916709 0.930569796
## spread_zoffset[1] 4.040845e-01 0.0256416257 1.044281517
## spread_zoffset[2] 4.490840e-01 0.0181800272 0.846101832
## spread_zoffset[3] 1.175208e-01 0.0157840572 0.857612550
## spread_zoffset[4] 6.188779e-01 0.0158046010 0.759206661
## spread_zoffset[5] 4.168727e-01 0.0193273716 0.904251598
## spread_zoffset[6] -7.495005e-01 0.0159739335 0.808797438
## spread_zoffset[7] 4.968311e-01 0.0166470156 0.791261362
## spread_zoffset[8] 4.460710e-01 0.0277448329 1.046036976
## spread_zoffset[9] -8.457427e-01 0.0151003762 0.809567032
## spread_zoffset[10] 6.970731e-01 0.0287136153 1.003933247
## spread_zoffset[11] -7.070511e-02 0.0186155651 0.929912502
## spread_zoffset[12] -4.314152e-01 0.0150065687 0.775725599
## spread_zoffset[13] -4.536415e-01 0.0145232149 0.805171131
## spread_zoffset[14] -5.578952e-02 0.0191699985 1.038267921
## spread_zoffset[15] 5.981885e-01 0.0215795295 0.936906259
## spread_zoffset[16] -7.724797e-01 0.0150631526 0.805259195
## spread_zoffset[17] 6.885550e-02 0.0159977297 0.878275029
## spread_zoffset[18] -5.298818e-01 0.0168291513 0.810223711
## spread_zoffset[19] 1.392026e-02 0.0194675850 1.005984815
## spread_zoffset[20] 1.949887e-02 0.0142705936 0.751592153
## spread_zoffset[21] 4.363021e-01 0.0156178242 0.747771967
## spread_zoffset[22] -2.649252e-01 0.0152806566 0.757239309
## spread_zoffset[23] 2.683945e-01 0.0165198255 0.810507273
## spread_zoffset[24] 3.296295e-02 0.0173391314 0.999583608
## spread_zoffset[25] 7.187806e-01 0.0190612245 0.914408862
## spread_zoffset[26] 2.776720e-01 0.0227052432 1.018392603
## spread_zoffset[27] -2.023958e-01 0.0143134550 0.727483448
## spread_zoffset[28] 5.565484e-01 0.0161043560 0.814196970
## spread_zoffset[29] 2.129071e-01 0.0167927223 0.755364717
## spread_zoffset[30] 3.349508e-01 0.0333266262 1.019457602
## spread_zoffset[31] -5.026399e-01 0.0162207451 0.812485983
## spread_zoffset[32] 3.240571e-01 0.0281108599 1.080523255
## spread_zoffset[33] 4.011530e-01 0.0135719344 0.729066463
## spread_zoffset[34] 8.790139e-02 0.0150029712 0.802153814
## spread_zoffset[35] -8.356861e-02 0.0142141121 0.839234183
## spread_zoffset[36] -1.020240e-01 0.0157096847 0.790667264
## spread_zoffset[37] 4.201852e-01 0.0215601709 1.037786309
## spread_zoffset[38] 2.151625e-01 0.0140624638 0.768550968
## spread_zoffset[39] 1.246259e-01 0.0158629983 0.820949226
## spread_zoffset[40] -7.085356e-01 0.0156346744 0.783886499
## spread_zoffset[41] -6.650859e-02 0.0204165949 0.935347692
## spread_zoffset[42] 2.247453e-01 0.0226296472 0.993737450
## spread_zoffset[43] 3.692482e-01 0.0242232673 1.049788754
## spread_zoffset[44] -1.244181e-01 0.0128175213 0.760508079
## spread_zoffset[45] -3.940355e-01 0.0160715072 0.803511430
## spread_zoffset[46] -2.477399e-02 0.0200437829 1.026715672
## spread_zoffset[47] -1.179306e+00 0.0162680407 0.822717746
## spread_zoffset[48] -3.286503e-01 0.0155671176 0.804143677
## spread_zoffset[49] -5.861948e-01 0.0148951339 0.796189179
## spread_zoffset[50] 4.314825e-01 0.0177057347 0.992899689
## spread_zoffset[51] 5.362392e-01 0.0199029234 0.847628323
## spread_zoffset[52] 7.016614e-01 0.0154283457 0.780380148
## spread_zoffset[53] -7.242438e-01 0.0165708537 0.862763252
## spread_zoffset[54] -2.020375e-01 0.0152206228 0.792742301
## spread_zoffset[55] 6.345987e-03 0.0146175581 0.752306027
## spread_zoffset[56] -8.054125e-01 0.0160309429 0.840451405
## spread_zoffset[57] -6.569633e-01 0.0132762218 0.795550856
## spread_zoffset[58] -6.615523e-01 0.0161654735 0.798095538
## spread_zoffset[59] 5.265475e-01 0.0147905738 0.731024833
## spread_zoffset[60] 4.028945e-01 0.0193997100 0.920241899
## spread_zoffset[61] 2.908079e-01 0.0155245155 0.728660257
## spread_zoffset[62] -4.222582e-01 0.0176939034 0.937276562
## spread_zoffset[63] 5.327210e-01 0.0181095265 0.840530326
## spread_zoffset[64] 6.496609e-01 0.0188342254 0.827378019
## spread_zoffset[65] 6.017323e-01 0.0124073264 0.716953335
## spread_zoffset[66] 3.272521e-01 0.0174693428 0.800467863
## spread_zoffset[67] -6.436348e-01 0.0142975884 0.799945017
## spread_zoffset[68] 1.031541e-01 0.0242189375 0.998207728
## spread_zoffset[69] -1.364609e+00 0.0168300951 0.815109278
## spread_zoffset[70] 1.178042e-02 0.0165659083 0.841973497
## spread_zoffset[71] 5.305795e-01 0.0191113392 0.866057786
## spread_zoffset[72] 3.553164e-01 0.0185831445 0.975360557
## spread_zoffset[73] 5.174700e-02 0.0170713673 0.885635803
## spread_zoffset[74] 1.164035e-02 0.0164387515 0.797363092
## spread_zoffset[75] 2.731711e-01 0.0122642664 0.737691019
## spread_zoffset[76] 1.436561e-02 0.0213188406 0.955172294
## spread_zoffset[77] -1.689875e+00 0.0225882365 0.846049983
## spread_zoffset[78] -3.546576e-01 0.0139561623 0.762443921
## spread_zoffset[79] 2.347579e-01 0.0146836689 0.814924426
## spread_zoffset[80] 2.398022e-01 0.0206647096 0.921124376
## spread_zoffset[81] 1.244355e-01 0.0165680715 0.867337975
## spread_zoffset[82] 4.812325e-01 0.0175100567 0.780999685
## spread_zoffset[83] -1.751925e-01 0.0153899824 0.794977982
## spread_zoffset[84] -9.208259e-01 0.0158711176 0.834646782
## spread_zoffset[85] -1.020572e+00 0.0162312504 0.844499759
## spread_zoffset[86] -3.181043e-01 0.0292752120 1.013439115
## spread_zoffset[87] 2.174256e-01 0.0285458490 1.116235482
## spread_zoffset[88] 3.330073e-01 0.0162522929 0.778813209
## spread_zoffset[89] 3.784042e-01 0.0222692847 0.950514502
## spread_zoffset[90] 9.394269e-01 0.0179376799 0.823496538
## spread_zoffset[91] -6.662734e-01 0.0135925297 0.806245843
## spread_zoffset[92] 3.226376e-01 0.0162038199 0.773785968
## spread_zoffset[93] 3.975983e-01 0.0296515746 1.016513855
## spread_zoffset[94] 4.738809e-02 0.0215007484 1.016795381
## spread_zoffset[95] 2.424367e-01 0.0153583626 0.764831868
## spread_zoffset[96] 7.789003e-02 0.0369108292 1.125148468
## spread_zoffset[97] 1.574749e-01 0.0184211056 1.057006075
## spread_zoffset[98] -9.762846e-01 0.0196220165 0.852786997
## spread_zoffset[99] 6.153656e-01 0.0172188258 0.800509954
## spread_zoffset[100] 3.257359e-01 0.0148356032 0.746088224
## spread_zoffset[101] 9.852179e-01 0.0228124226 0.928978797
## spread_zoffset[102] -3.062543e-01 0.0140868977 0.776869407
## spread_zoffset[103] 1.537346e-01 0.0192063741 1.032597706
## spread_zoffset[104] -1.969986e-01 0.0155580943 0.819615622
## spread_zoffset[105] 1.733508e-02 0.0175474864 0.814227583
## spread_zoffset[106] 5.092781e-01 0.0177444109 0.858870787
## spread_zoffset[107] 7.652216e-01 0.0287543120 0.869894006
## spread_zoffset[108] 5.808476e-02 0.0172966663 0.786637922
## spread_zoffset[109] -3.307785e-02 0.0135835498 0.772353292
## spread_zoffset[110] 4.558518e-01 0.0308045363 1.042134767
## spread_zoffset[111] -2.519096e-01 0.0164127608 0.760796541
## spread_zoffset[112] -2.401141e-01 0.0155102460 0.779341621
## spread_zoffset[113] -4.414138e-01 0.0162225033 0.802913085
## spread_zoffset[114] 3.127212e-01 0.0297503334 1.053184057
## spread_zoffset[115] -5.698434e-02 0.0148729402 0.783580783
## spread_zoffset[116] -2.633166e-01 0.0151088776 0.812026184
## spread_zoffset[117] 2.827028e-01 0.0193763956 0.867598941
## spread_zoffset[118] 2.196846e-01 0.0231055330 1.039378889
## spread_zoffset[119] -3.335949e-01 0.0147207696 0.760809709
## spread_zoffset[120] 6.357032e-01 0.0142736374 0.727162882
## spread_zoffset[121] -3.004599e-01 0.0157453621 0.751348138
## spread_zoffset[122] -7.894109e-01 0.0125800936 0.757208732
## spread_zoffset[123] -2.679996e-01 0.0133534015 0.765352328
## spread_zoffset[124] 3.234768e-01 0.0142029278 0.740325467
## spread_zoffset[125] 1.808265e-02 0.0142268956 0.725270106
## spread_zoffset[126] 2.649743e-01 0.0249858493 0.987567229
## spread_zoffset[127] 6.096536e-01 0.0180314903 0.860949652
## spread_zoffset[128] -2.202442e-01 0.0230209885 1.013111688
## spread_zoffset[129] -6.997819e-01 0.0135907413 0.813008496
## spread_zoffset[130] 5.799320e-01 0.0165391583 0.775864817
## spread_zoffset[131] -5.898301e-01 0.0142926592 0.783484167
## spread_zoffset[132] 3.481504e-01 0.0269385465 1.044860069
## spread_zoffset[133] -4.002112e-01 0.0149020712 0.801038819
## spread_zoffset[134] 2.904461e-01 0.0149826413 0.746172806
## spread_zoffset[135] -7.894409e-02 0.0189024825 0.983451790
## spread_zoffset[136] 8.059051e-01 0.0158186105 0.752138708
## spread_zoffset[137] -3.956006e-01 0.0137384757 0.792649959
## spread_zoffset[138] -1.465901e-01 0.0152461440 0.753929423
## spread_zoffset[139] 3.258611e-01 0.0169824491 0.752093620
## spread_zoffset[140] -5.928110e-01 0.0138296325 0.794400246
## spread_zoffset[141] 4.492808e-01 0.0186174120 0.838085221
## spread_zoffset[142] -2.033806e-01 0.0260867159 1.079531605
## spread_zoffset[143] -3.805748e-01 0.0144172994 0.807284710
## spread_zoffset[144] 1.471646e-01 0.0150411220 0.806880638
## spread_zoffset[145] 2.540874e-01 0.0264194905 1.061089894
## spread_zoffset[146] 1.353883e-01 0.0231292095 0.963298934
## spread_zoffset[147] -1.417668e+00 0.0159614921 0.887898121
## spread_zoffset[148] 2.693586e-01 0.0238552708 0.999499567
## spread_zoffset[149] -4.244872e-01 0.0150394978 0.724049194
## spread_zoffset[150] -4.445115e-01 0.0167352714 0.775049593
## lapse_zoffset[1] 1.193495e+00 0.0142892238 0.373781320
## lapse_zoffset[2] -8.410605e-02 0.0210131502 0.832119935
## lapse_zoffset[3] 1.174912e-01 0.0196010306 0.681507224
## lapse_zoffset[4] -3.890512e-01 0.0158455987 0.749046378
## lapse_zoffset[5] 1.178403e-01 0.0224103077 0.697628265
## lapse_zoffset[6] -5.646686e-01 0.0156335548 0.741370613
## lapse_zoffset[7] -1.895730e-01 0.0206763447 0.814947778
## lapse_zoffset[8] 4.339784e-01 0.0275308938 0.660942834
## lapse_zoffset[9] -6.394117e-01 0.0145240442 0.726111875
## lapse_zoffset[10] 6.536631e-01 0.0318662197 0.709123757
## lapse_zoffset[11] 2.212155e-01 0.0198070678 0.699168946
## lapse_zoffset[12] -5.876531e-01 0.0160216629 0.702275479
## lapse_zoffset[13] -6.128570e-01 0.0151484596 0.695937184
## lapse_zoffset[14] 1.404611e+00 0.0097379698 0.253378762
## lapse_zoffset[15] 3.017964e-01 0.0287199999 0.796429399
## lapse_zoffset[16] -7.298381e-01 0.0147609614 0.732166908
## lapse_zoffset[17] -2.508128e-01 0.0174453686 0.756888475
## lapse_zoffset[18] -6.041101e-01 0.0165033216 0.730216766
## lapse_zoffset[19] 1.940475e+00 0.0127724103 0.259022110
## lapse_zoffset[20] -5.369452e-01 0.0150764446 0.765743857
## lapse_zoffset[21] -3.927495e-01 0.0172735051 0.751833576
## lapse_zoffset[22] -6.780606e-01 0.0151274677 0.708176187
## lapse_zoffset[23] -2.067841e-01 0.0202908518 0.811848090
## lapse_zoffset[24] 2.109710e+00 0.0130146854 0.264188788
## lapse_zoffset[25] 3.337155e-01 0.0239142195 0.749801477
## lapse_zoffset[26] 3.656762e-01 0.0271766971 0.684929068
## lapse_zoffset[27] -5.675058e-01 0.0167978400 0.741904596
## lapse_zoffset[28] -1.028011e-01 0.0186897570 0.770488045
## lapse_zoffset[29] -4.224066e-01 0.0153732074 0.755901189
## lapse_zoffset[30] 9.382733e-01 0.0233042964 0.471805580
## lapse_zoffset[31] -5.547477e-01 0.0181984886 0.756462343
## lapse_zoffset[32] 1.192735e+00 0.0165271509 0.394109166
## lapse_zoffset[33] -4.541349e-01 0.0162255288 0.781556364
## lapse_zoffset[34] -3.692591e-01 0.0159848712 0.760227214
## lapse_zoffset[35] -3.863123e-01 0.0163778590 0.752502352
## lapse_zoffset[36] -5.176015e-01 0.0155422096 0.765309663
## lapse_zoffset[37] 1.390523e+00 0.0129352425 0.341070460
## lapse_zoffset[38] -3.963935e-01 0.0170403540 0.797974200
## lapse_zoffset[39] -5.043856e-01 0.0164204833 0.690860074
## lapse_zoffset[40] -6.714085e-01 0.0153478052 0.695456281
## lapse_zoffset[41] -3.770979e-02 0.0204641524 0.744905088
## lapse_zoffset[42] 1.511241e+00 0.0100391195 0.248684526
## lapse_zoffset[43] 5.977596e-01 0.0252808074 0.706724327
## lapse_zoffset[44] -4.838180e-01 0.0150364289 0.772844047
## lapse_zoffset[45] -5.938989e-01 0.0154527984 0.715646812
## lapse_zoffset[46] 2.069608e+00 0.0132133444 0.265048137
## lapse_zoffset[47] -7.583074e-01 0.0154572050 0.686514487
## lapse_zoffset[48] -5.986918e-01 0.0163302923 0.760192898
## lapse_zoffset[49] -6.482915e-01 0.0163230687 0.739144824
## lapse_zoffset[50] 1.495457e+00 0.0098652303 0.253515904
## lapse_zoffset[51] -2.541884e-01 0.0193797660 0.799392847
## lapse_zoffset[52] -1.522052e-01 0.0201321829 0.824457651
## lapse_zoffset[53] -5.826488e-01 0.0151353332 0.724722297
## lapse_zoffset[54] -4.903084e-01 0.0156009281 0.725875640
## lapse_zoffset[55] -5.223139e-01 0.0169769682 0.774727159
## lapse_zoffset[56] -6.519940e-01 0.0147550112 0.689545277
## lapse_zoffset[57] -7.387347e-01 0.0163688555 0.735708122
## lapse_zoffset[58] -6.251404e-01 0.0161470059 0.739427058
## lapse_zoffset[59] -3.548243e-01 0.0180538301 0.779379656
## lapse_zoffset[60] 2.451630e-01 0.0193100119 0.662707081
## lapse_zoffset[61] -4.651278e-01 0.0168457953 0.750648292
## lapse_zoffset[62] -8.347546e-02 0.0173328264 0.658319901
## lapse_zoffset[63] -1.360146e-01 0.0179685402 0.731731591
## lapse_zoffset[64] 5.219041e-02 0.0235682329 0.731230238
## lapse_zoffset[65] -4.995131e-01 0.0162205002 0.759190412
## lapse_zoffset[66] -2.013050e-01 0.0190495574 0.779127291
## lapse_zoffset[67] -6.777250e-01 0.0137503740 0.744266735
## lapse_zoffset[68] 6.921330e-01 0.0217463155 0.565730459
## lapse_zoffset[69] -6.483396e-01 0.0138721527 0.690494026
## lapse_zoffset[70] -4.318392e-01 0.0168429275 0.736802317
## lapse_zoffset[71] 7.237670e-02 0.0226083899 0.767470644
## lapse_zoffset[72] 1.716941e+00 0.0101762987 0.265045764
## lapse_zoffset[73] -7.785769e-02 0.0185463814 0.707320426
## lapse_zoffset[74] -5.272899e-01 0.0154771184 0.728196031
## lapse_zoffset[75] -4.814782e-01 0.0153642274 0.769052517
## lapse_zoffset[76] 2.272641e-01 0.0219226641 0.722058066
## lapse_zoffset[77] -7.025220e-01 0.0125173757 0.700921255
## lapse_zoffset[78] -5.353327e-01 0.0147507335 0.740883684
## lapse_zoffset[79] -4.309058e-01 0.0164799428 0.756978123
## lapse_zoffset[80] 2.126794e-01 0.0194927167 0.650925798
## lapse_zoffset[81] -1.591972e-01 0.0171339293 0.688130706
## lapse_zoffset[82] -2.430407e-01 0.0186680990 0.816124354
## lapse_zoffset[83] -5.725442e-01 0.0162209269 0.728286055
## lapse_zoffset[84] -6.235124e-01 0.0140480821 0.725195160
## lapse_zoffset[85] -6.474246e-01 0.0149641417 0.735382764
## lapse_zoffset[86] 9.042442e-01 0.0200116458 0.398201664
## lapse_zoffset[87] 1.021280e+00 0.0275511384 0.525891632
## lapse_zoffset[88] -3.219270e-01 0.0171537214 0.776618668
## lapse_zoffset[89] 4.378443e-01 0.0196523724 0.646356958
## lapse_zoffset[90] 6.816194e-02 0.0230635022 0.836722686
## lapse_zoffset[91] -6.084818e-01 0.0170259536 0.769821814
## lapse_zoffset[92] -3.571542e-01 0.0166063899 0.763719835
## lapse_zoffset[93] 6.851632e-01 0.0289196463 0.638424384
## lapse_zoffset[94] 1.500216e+00 0.0097224081 0.247232013
## lapse_zoffset[95] -4.514815e-01 0.0162932653 0.778113960
## lapse_zoffset[96] 1.143517e+00 0.0199167636 0.419595058
## lapse_zoffset[97] 1.932795e+00 0.0124309176 0.256451260
## lapse_zoffset[98] -7.474136e-01 0.0160890016 0.732469091
## lapse_zoffset[99] -1.769049e-01 0.0200828023 0.832433159
## lapse_zoffset[100] -4.108219e-01 0.0178340828 0.803403655
## lapse_zoffset[101] 2.751720e-01 0.0233106950 0.722556952
## lapse_zoffset[102] -6.095027e-01 0.0159439676 0.762057549
## lapse_zoffset[103] 1.660090e+00 0.0119290132 0.255117257
## lapse_zoffset[104] -5.105916e-01 0.0177844264 0.763696816
## lapse_zoffset[105] -3.570526e-01 0.0179522832 0.741043704
## lapse_zoffset[106] 5.295277e-02 0.0207807200 0.708516517
## lapse_zoffset[107] -1.932501e-01 0.0225954157 0.844933095
## lapse_zoffset[108] -5.290146e-01 0.0158157270 0.703815281
## lapse_zoffset[109] -5.061068e-01 0.0151052528 0.772199630
## lapse_zoffset[110] 1.109593e+00 0.0204966659 0.407124579
## lapse_zoffset[111] -5.411049e-01 0.0154557612 0.797589096
## lapse_zoffset[112] -5.792436e-01 0.0165632764 0.737332742
## lapse_zoffset[113] -6.430436e-01 0.0159721549 0.717233990
## lapse_zoffset[114] 1.080951e+00 0.0206578768 0.464002407
## lapse_zoffset[115] -5.483109e-01 0.0147848718 0.746864301
## lapse_zoffset[116] -4.943276e-01 0.0171857077 0.773338910
## lapse_zoffset[117] 2.083384e-01 0.0191422035 0.670676618
## lapse_zoffset[118] 1.434893e+00 0.0113520757 0.302906896
## lapse_zoffset[119] -5.928068e-01 0.0158272261 0.715598359
## lapse_zoffset[120] -4.396959e-01 0.0158316775 0.753929494
## lapse_zoffset[121] -6.460430e-01 0.0156653659 0.713985078
## lapse_zoffset[122] -5.634993e-01 0.0183820032 0.746118923
## lapse_zoffset[123] -5.176762e-01 0.0176924012 0.766208232
## lapse_zoffset[124] -4.131633e-01 0.0163126948 0.776762198
## lapse_zoffset[125] -5.133291e-01 0.0170922233 0.785881049
## lapse_zoffset[126] 4.691765e-01 0.0255801660 0.699303808
## lapse_zoffset[127] 9.256093e-02 0.0202365762 0.814070160
## lapse_zoffset[128] 1.472334e+00 0.0121678539 0.301248885
## lapse_zoffset[129] -6.291906e-01 0.0168409955 0.725039686
## lapse_zoffset[130] -9.464164e-02 0.0192068563 0.788990265
## lapse_zoffset[131] -5.248175e-01 0.0148570493 0.719321404
## lapse_zoffset[132] 6.661420e-01 0.0199122893 0.548671389
## lapse_zoffset[133] -6.248505e-01 0.0154060825 0.752003077
## lapse_zoffset[134] -3.996598e-01 0.0185550834 0.805540752
## lapse_zoffset[135] 1.856299e+00 0.0107183412 0.245215860
## lapse_zoffset[136] -3.002751e-01 0.0176748782 0.801018420
## lapse_zoffset[137] -5.064425e-01 0.0150882949 0.734397574
## lapse_zoffset[138] -4.676429e-01 0.0154577554 0.748368126
## lapse_zoffset[139] -3.393408e-01 0.0185182170 0.803829585
## lapse_zoffset[140] -6.021896e-01 0.0163534584 0.771734992
## lapse_zoffset[141] -2.430297e-01 0.0188197671 0.781236251
## lapse_zoffset[142] 5.640368e-01 0.0198235471 0.585266408
## lapse_zoffset[143] -5.609870e-01 0.0169889484 0.766879082
## lapse_zoffset[144] -1.502922e-01 0.0188104271 0.755852467
## lapse_zoffset[145] 6.639891e-01 0.0212462228 0.539671012
## lapse_zoffset[146] 4.257643e-01 0.0225117788 0.676705045
## lapse_zoffset[147] -7.792449e-01 0.0145451608 0.699737993
## lapse_zoffset[148] 5.802248e-01 0.0215117035 0.610408835
## lapse_zoffset[149] -5.774494e-01 0.0145944676 0.722189918
## lapse_zoffset[150] -5.658090e-01 0.0152794601 0.749502462
## threshold[1] 2.620343e+00 0.0069441513 0.351480326
## threshold[2] 2.444291e+00 0.0058200660 0.300583279
## threshold[3] 2.362572e+00 0.0041081180 0.270588307
## threshold[4] 2.384648e+00 0.0055492060 0.290419005
## threshold[5] 2.370070e+00 0.0054673643 0.305761204
## threshold[6] 2.277109e+00 0.0055361826 0.239129926
## threshold[7] 2.472335e+00 0.0063281210 0.314049388
## threshold[8] 2.323102e+00 0.0051265155 0.290502410
## threshold[9] 2.428907e+00 0.0065061130 0.251032895
## threshold[10] 2.396663e+00 0.0055733419 0.301160468
## threshold[11] 2.397133e+00 0.0048681004 0.265301994
## threshold[12] 2.376203e+00 0.0049475996 0.274267398
## threshold[13] 2.548445e+00 0.0048996127 0.285010118
## threshold[14] 2.347145e+00 0.0058546380 0.317251737
## threshold[15] 2.513893e+00 0.0073491675 0.323574083
## threshold[16] 2.284926e+00 0.0046851806 0.264184841
## threshold[17] 2.335827e+00 0.0046511378 0.248120657
## threshold[18] 2.405588e+00 0.0069627238 0.271391838
## threshold[19] 2.585808e+00 0.0062982349 0.337209903
## threshold[20] 2.564256e+00 0.0050375875 0.284284278
## threshold[21] 2.418567e+00 0.0066903353 0.309205131
## threshold[22] 2.303722e+00 0.0046387613 0.266691397
## threshold[23] 2.494869e+00 0.0081102745 0.309371773
## threshold[24] 2.576463e+00 0.0063775590 0.327837146
## threshold[25] 2.739882e+00 0.0128926788 0.393990096
## threshold[26] 2.429279e+00 0.0073549648 0.332832549
## threshold[27] 2.619852e+00 0.0057702066 0.302575478
## threshold[28] 2.666285e+00 0.0079461089 0.339738636
## threshold[29] 2.779981e+00 0.0130447258 0.372709046
## threshold[30] 2.462460e+00 0.0094611524 0.352107172
## threshold[31] 2.333861e+00 0.0045677951 0.258242028
## threshold[32] 2.634827e+00 0.0079843678 0.359737383
## threshold[33] 2.457111e+00 0.0065613388 0.296485065
## threshold[34] 2.548867e+00 0.0051173546 0.282666492
## threshold[35] 2.611400e+00 0.0061581334 0.301706996
## threshold[36] 2.276085e+00 0.0060159734 0.262611696
## threshold[37] 2.430884e+00 0.0069255613 0.334143099
## threshold[38] 2.454123e+00 0.0064574568 0.294570704
## threshold[39] 2.238968e+00 0.0054362234 0.273596782
## threshold[40] 2.403508e+00 0.0075293808 0.264398204
## threshold[41] 2.571189e+00 0.0057993553 0.290193575
## threshold[42] 2.421667e+00 0.0073450956 0.344324332
## threshold[43] 2.458830e+00 0.0062665283 0.302673846
## threshold[44] 2.313236e+00 0.0046656149 0.253628455
## threshold[45] 2.333213e+00 0.0051405190 0.289966442
## threshold[46] 2.567539e+00 0.0063741503 0.327624584
## threshold[47] 2.192984e+00 0.0057627828 0.262592987
## threshold[48] 2.393289e+00 0.0069796436 0.268849757
## threshold[49] 2.388081e+00 0.0068598629 0.261658675
## threshold[50] 2.429219e+00 0.0089438270 0.381947904
## threshold[51] 2.373633e+00 0.0063196051 0.311900090
## threshold[52] 2.482486e+00 0.0075041246 0.338237007
## threshold[53] 2.230567e+00 0.0057450403 0.260537867
## threshold[54] 2.444607e+00 0.0068740647 0.302616436
## threshold[55] 2.680300e+00 0.0081377906 0.317537155
## threshold[56] 2.457815e+00 0.0065022157 0.267165908
## threshold[57] 2.226239e+00 0.0051155427 0.263687528
## threshold[58] 2.435587e+00 0.0064341227 0.293278284
## threshold[59] 2.547383e+00 0.0133522459 0.381449495
## threshold[60] 2.482813e+00 0.0097651471 0.331341018
## threshold[61] 2.495039e+00 0.0088089715 0.356856896
## threshold[62] 2.345134e+00 0.0050210385 0.288690566
## threshold[63] 2.435469e+00 0.0074530929 0.336882081
## threshold[64] 2.484185e+00 0.0106603006 0.348951813
## threshold[65] 2.492686e+00 0.0049483761 0.283565643
## threshold[66] 2.540352e+00 0.0122428757 0.382797957
## threshold[67] 2.430495e+00 0.0063072007 0.265702446
## threshold[68] 2.666211e+00 0.0080619014 0.341393926
## threshold[69] 2.269392e+00 0.0062570535 0.238318629
## threshold[70] 2.392918e+00 0.0074726242 0.268649197
## threshold[71] 2.582944e+00 0.0059070323 0.298816822
## threshold[72] 2.480655e+00 0.0094085162 0.354488208
## threshold[73] 2.398607e+00 0.0061667837 0.304975326
## threshold[74] 2.533717e+00 0.0048633178 0.276624842
## threshold[75] 2.626489e+00 0.0071571460 0.303919953
## threshold[76] 2.375654e+00 0.0054949871 0.281949780
## threshold[77] 2.157242e+00 0.0088341891 0.239974517
## threshold[78] 2.425039e+00 0.0047096099 0.283120406
## threshold[79] 2.403806e+00 0.0074059116 0.275727481
## threshold[80] 2.455312e+00 0.0070997976 0.329534370
## threshold[81] 2.277788e+00 0.0048925015 0.288400283
## threshold[82] 2.673033e+00 0.0080152365 0.346082947
## threshold[83] 2.641450e+00 0.0060249929 0.290649401
## threshold[84] 2.522982e+00 0.0049748000 0.263208077
## threshold[85] 2.267263e+00 0.0055832524 0.236001958
## threshold[86] 2.383599e+00 0.0059970595 0.302620236
## threshold[87] 2.443200e+00 0.0061175848 0.314633678
## threshold[88] 2.632070e+00 0.0066348883 0.298462624
## threshold[89] 2.657540e+00 0.0079597384 0.337551365
## threshold[90] 2.566535e+00 0.0110132162 0.367823715
## threshold[91] 2.247822e+00 0.0065975010 0.252814648
## threshold[92] 2.463389e+00 0.0081654393 0.335550988
## threshold[93] 2.406514e+00 0.0050067658 0.298383012
## threshold[94] 2.388259e+00 0.0069108976 0.323625822
## threshold[95] 2.416205e+00 0.0060349239 0.295390963
## threshold[96] 2.351537e+00 0.0057274982 0.302863625
## threshold[97] 2.535140e+00 0.0061180656 0.318627780
## threshold[98] 2.208796e+00 0.0052940890 0.259063279
## threshold[99] 2.665317e+00 0.0075232261 0.336896681
## threshold[100] 2.431318e+00 0.0054997749 0.290690863
## threshold[101] 2.390770e+00 0.0066439564 0.328350707
## threshold[102] 2.498663e+00 0.0051084291 0.275326408
## threshold[103] 2.592193e+00 0.0067548374 0.339667284
## threshold[104] 2.293287e+00 0.0058342855 0.268190996
## threshold[105] 2.545561e+00 0.0049614597 0.273639342
## threshold[106] 2.432842e+00 0.0066073313 0.316711381
## threshold[107] 3.053578e+00 0.0322613147 0.610298625
## threshold[108] 2.324027e+00 0.0049767101 0.282070726
## threshold[109] 2.371419e+00 0.0047230372 0.272189876
## threshold[110] 2.442365e+00 0.0086862050 0.352499243
## threshold[111] 2.425735e+00 0.0054780268 0.287448263
## threshold[112] 2.394966e+00 0.0065135809 0.295250514
## threshold[113] 2.274032e+00 0.0049579383 0.269820492
## threshold[114] 2.373717e+00 0.0051384014 0.288263786
## threshold[115] 2.312565e+00 0.0048060367 0.252971286
## threshold[116] 2.403473e+00 0.0045668362 0.267280827
## threshold[117] 2.661203e+00 0.0076162677 0.324829778
## threshold[118] 2.423661e+00 0.0060141138 0.316250093
## threshold[119] 2.480785e+00 0.0087012682 0.328692935
## threshold[120] 2.384167e+00 0.0046518348 0.265268079
## threshold[121] 2.387470e+00 0.0059649972 0.288853294
## threshold[122] 2.368571e+00 0.0038192179 0.243400132
## threshold[123] 2.383549e+00 0.0046889830 0.278415478
## threshold[124] 2.499698e+00 0.0082201249 0.311733452
## threshold[125] 2.686776e+00 0.0079262887 0.328740256
## threshold[126] 2.471259e+00 0.0064362433 0.324092674
## threshold[127] 2.527737e+00 0.0106123839 0.332908064
## threshold[128] 2.370369e+00 0.0056589376 0.302786030
## threshold[129] 2.246829e+00 0.0065009285 0.247147860
## threshold[130] 2.672547e+00 0.0087357635 0.338560384
## threshold[131] 2.550734e+00 0.0051977636 0.271494438
## threshold[132] 2.442915e+00 0.0074340222 0.331236301
## threshold[133] 2.331355e+00 0.0050291549 0.288661139
## threshold[134] 2.492466e+00 0.0078982697 0.316199249
## threshold[135] 2.368875e+00 0.0058765779 0.328582037
## threshold[136] 2.498952e+00 0.0083558929 0.343491767
## threshold[137] 2.519869e+00 0.0047979281 0.261160291
## threshold[138] 2.647322e+00 0.0067465649 0.311086558
## threshold[139] 2.548952e+00 0.0095745242 0.343972714
## threshold[140] 2.349875e+00 0.0046828531 0.269250041
## threshold[141] 2.383722e+00 0.0061264925 0.297320959
## threshold[142] 2.636515e+00 0.0066941512 0.328271065
## threshold[143] 2.440615e+00 0.0049574150 0.272578317
## threshold[144] 2.424591e+00 0.0064887320 0.306596226
## threshold[145] 2.373934e+00 0.0062198267 0.296821242
## threshold[146] 2.479225e+00 0.0065394951 0.305386677
## threshold[147] 2.105106e+00 0.0095390935 0.258721953
## threshold[148] 2.600631e+00 0.0056966617 0.306560056
## threshold[149] 2.443392e+00 0.0058582323 0.271231212
## threshold[150] 2.349233e+00 0.0047147630 0.268295281
## spread[1] 1.824541e+00 0.0180566330 0.580297272
## spread[2] 1.853861e+00 0.0119301288 0.421861280
## spread[3] 1.708394e+00 0.0110248064 0.414239845
## spread[4] 2.181866e+00 0.0118587836 0.439498593
## spread[5] 2.106796e+00 0.0149573340 0.548211695
## spread[6] 1.348277e+00 0.0061980919 0.289811045
## spread[7] 1.875669e+00 0.0099589580 0.405102180
## spread[8] 2.151093e+00 0.0268668613 0.653341807
## spread[9] 1.274473e+00 0.0081089682 0.284783082
## spread[10] 2.027651e+00 0.0263110742 0.620158379
## spread[11] 1.632741e+00 0.0098429040 0.421687416
## spread[12] 1.664456e+00 0.0071804958 0.355854979
## spread[13] 1.411999e+00 0.0055247694 0.300786253
## spread[14] 1.880700e+00 0.0139223975 0.599071822
## spread[15] 1.952503e+00 0.0181050480 0.513747437
## spread[16] 1.521628e+00 0.0065456212 0.327377110
## spread[17] 1.681603e+00 0.0079806580 0.388712845
## spread[18] 1.386060e+00 0.0059122975 0.297677714
## spread[19] 1.633403e+00 0.0112008433 0.500233130
## spread[20] 1.593042e+00 0.0059037876 0.317847695
## spread[21] 2.077178e+00 0.0096685672 0.409620458
## spread[22] 1.731364e+00 0.0061516133 0.347658743
## spread[23] 1.763085e+00 0.0092389435 0.381944863
## spread[24] 1.636383e+00 0.0094079634 0.482965469
## spread[25] 1.948483e+00 0.0160310158 0.499597699
## spread[26] 2.036982e+00 0.0167486735 0.579477352
## spread[27] 1.505466e+00 0.0060937611 0.299106464
## spread[28] 1.849715e+00 0.0096247146 0.404197416
## spread[29] 1.683968e+00 0.0082104128 0.343006145
## spread[30] 2.094959e+00 0.0333928516 0.677992738
## spread[31] 1.439725e+00 0.0061664196 0.311977478
## spread[32] 1.792039e+00 0.0233516451 0.617443050
## spread[33] 1.760472e+00 0.0070418050 0.341430357
## spread[34] 1.627920e+00 0.0065275556 0.337606440
## spread[35] 1.561159e+00 0.0061149124 0.339206543
## spread[36] 1.595833e+00 0.0063262061 0.334023312
## spread[37] 1.890057e+00 0.0207041211 0.608660881
## spread[38] 1.735940e+00 0.0080651898 0.365663616
## spread[39] 1.928837e+00 0.0091437845 0.436884038
## spread[40] 1.320136e+00 0.0071409396 0.281724631
## spread[41] 1.578659e+00 0.0085393363 0.400323106
## spread[42] 2.017089e+00 0.0171922049 0.602630646
## spread[43] 1.858384e+00 0.0197319008 0.561549398
## spread[44] 1.586410e+00 0.0056470348 0.318999740
## spread[45] 1.677945e+00 0.0066278435 0.354312769
## spread[46] 1.607583e+00 0.0093916129 0.459895626
## spread[47] 1.369913e+00 0.0082234777 0.325149496
## spread[48] 1.463813e+00 0.0062649258 0.327342432
## spread[49] 1.361874e+00 0.0053457655 0.285402447
## spread[50] 2.133386e+00 0.0179670395 0.642264201
## spread[51] 2.149122e+00 0.0147574482 0.485900577
## spread[52] 1.976580e+00 0.0113839454 0.425973993
## spread[53] 1.540234e+00 0.0070152754 0.350314478
## spread[54] 1.766636e+00 0.0078658507 0.373516636
## spread[55] 1.592808e+00 0.0065630123 0.320085118
## spread[56] 1.291474e+00 0.0065639860 0.299394802
## spread[57] 1.565336e+00 0.0065454512 0.338287015
## spread[58] 1.563575e+00 0.0070464485 0.334460775
## spread[59] 2.130860e+00 0.0124209702 0.439408825
## spread[60] 2.093758e+00 0.0143944356 0.546863096
## spread[61] 2.003407e+00 0.0085601970 0.397575983
## spread[62] 1.679319e+00 0.0092419961 0.432332249
## spread[63] 2.148451e+00 0.0135781451 0.489428128
## spread[64] 2.225328e+00 0.0188517711 0.526697354
## spread[65] 1.858006e+00 0.0078561824 0.371131383
## spread[66] 2.033383e+00 0.0103100204 0.439926795
## spread[67] 1.343799e+00 0.0062659584 0.286087027
## spread[68] 1.666697e+00 0.0145277866 0.489247164
## spread[69] 1.151362e+00 0.0076265386 0.269947373
## spread[70] 1.599324e+00 0.0070636262 0.362223184
## spread[71] 1.845012e+00 0.0105289672 0.445591267
## spread[72] 1.844535e+00 0.0158306458 0.552510972
## spread[73] 1.907062e+00 0.0115821955 0.469335561
## spread[74] 1.594904e+00 0.0068526715 0.342548445
## spread[75] 1.705479e+00 0.0067900264 0.330833506
## spread[76] 1.672892e+00 0.0116598088 0.435531457
## spread[77] 1.058922e+00 0.0099957516 0.268287463
## spread[78] 1.493882e+00 0.0056334643 0.300838129
## spread[79] 1.690474e+00 0.0072630096 0.361321524
## spread[80] 2.008202e+00 0.0134772162 0.529891005
## spread[81] 1.935477e+00 0.0105584614 0.472489676
## spread[82] 1.804968e+00 0.0084019994 0.387843890
## spread[83] 1.520904e+00 0.0062475527 0.320968304
## spread[84] 1.253651e+00 0.0067632199 0.286783947
## spread[85] 1.256246e+00 0.0069754331 0.289719328
## spread[86] 1.746418e+00 0.0205985753 0.535921565
## spread[87] 1.809061e+00 0.0293065780 0.629018566
## spread[88] 1.734528e+00 0.0073846120 0.358202442
## spread[89] 1.788940e+00 0.0128665554 0.486973458
## spread[90] 2.114895e+00 0.0176109042 0.491914479
## spread[91] 1.381125e+00 0.0053059354 0.299858681
## spread[92] 2.020352e+00 0.0089306989 0.418376083
## spread[93] 1.880749e+00 0.0266455217 0.576891994
## spread[94] 1.928459e+00 0.0163027841 0.599501312
## spread[95] 1.745093e+00 0.0073356315 0.349861549
## spread[96] 1.742731e+00 0.0266664858 0.626259606
## spread[97] 1.692775e+00 0.0106704160 0.505586152
## spread[98] 1.444080e+00 0.0082872905 0.338315757
## spread[99] 1.870413e+00 0.0101994083 0.397577742
## spread[100] 1.784097e+00 0.0079515179 0.357402943
## spread[101] 2.455294e+00 0.0246683359 0.665417075
## spread[102] 1.467535e+00 0.0059919234 0.313501444
## spread[103] 1.694708e+00 0.0119229078 0.525844844
## spread[104] 1.765734e+00 0.0077632496 0.388312500
## spread[105] 1.598467e+00 0.0067205751 0.343757401
## spread[106] 2.142136e+00 0.0153692176 0.516116743
## spread[107] 1.966713e+00 0.0189748348 0.472957470
## spread[108] 1.884706e+00 0.0072207597 0.386404568
## spread[109] 1.625674e+00 0.0062613457 0.330860756
## spread[110] 2.172059e+00 0.0315017645 0.725774867
## spread[111] 1.533595e+00 0.0064562203 0.313344500
## spread[112] 1.745851e+00 0.0065681744 0.360051139
## spread[113] 1.660022e+00 0.0068091078 0.363692433
## spread[114] 1.844697e+00 0.0241494851 0.609579792
## spread[115] 1.615637e+00 0.0066463136 0.332460057
## spread[116] 1.534408e+00 0.0064408432 0.331631833
## spread[117] 1.730302e+00 0.0104057651 0.427093743
## spread[118] 1.788706e+00 0.0175848026 0.568829362
## spread[119] 1.704217e+00 0.0065539011 0.346679829
## spread[120] 1.934746e+00 0.0107363540 0.385651762
## spread[121] 1.714334e+00 0.0064877298 0.338257240
## spread[122] 1.335885e+00 0.0047339848 0.274731084
## spread[123] 1.529570e+00 0.0063656366 0.317145052
## spread[124] 1.784522e+00 0.0077024225 0.358005599
## spread[125] 1.593680e+00 0.0062740952 0.314069731
## spread[126] 1.790170e+00 0.0152462600 0.493297473
## spread[127] 1.947118e+00 0.0139623617 0.462353279
## spread[128] 1.583195e+00 0.0191623504 0.514400343
## spread[129] 1.366903e+00 0.0063738546 0.298388386
## spread[130] 1.852028e+00 0.0107809027 0.388491712
## spread[131] 1.362949e+00 0.0059572875 0.294883178
## spread[132] 2.097872e+00 0.0232393936 0.652274578
## spread[133] 1.674246e+00 0.0063838695 0.360253376
## spread[134] 1.768296e+00 0.0077049290 0.347595610
## spread[135] 1.855434e+00 0.0116236919 0.533795387
## spread[136] 2.025335e+00 0.0129182411 0.412878971
## spread[137] 1.434830e+00 0.0054125736 0.303660114
## spread[138] 1.528902e+00 0.0062359723 0.310389872
## spread[139] 1.784671e+00 0.0108790028 0.350724260
## spread[140] 1.407377e+00 0.0050749013 0.299062746
## spread[141] 2.105257e+00 0.0111957758 0.492723838
## spread[142] 1.542549e+00 0.0123290737 0.464112688
## spread[143] 1.486324e+00 0.0060716396 0.314390475
## spread[144] 1.940411e+00 0.0089511317 0.429328177
## spread[145] 2.043201e+00 0.0243591941 0.629578809
## spread[146] 1.731750e+00 0.0156314271 0.480827234
## spread[147] 1.291197e+00 0.0096114578 0.331343652
## spread[148] 1.746217e+00 0.0144039183 0.509444537
## spread[149] 1.418546e+00 0.0053674896 0.273591786
## spread[150] 1.460797e+00 0.0062780616 0.302220014
## lapse[1] 1.036191e-01 0.0011176423 0.040866097
## lapse[2] 1.740382e-02 0.0004769875 0.020177750
## lapse[3] 1.897936e-02 0.0003682902 0.018082018
## lapse[4] 1.386077e-02 0.0004162981 0.016794272
## lapse[5] 2.924525e-02 0.0006512165 0.025853881
## lapse[6] 6.475365e-03 0.0001918962 0.008813984
## lapse[7] 1.445809e-02 0.0003999735 0.017630948
## lapse[8] 4.658705e-02 0.0011169528 0.032591807
## lapse[9] 6.164913e-03 0.0001647733 0.007999902
## lapse[10] 4.804814e-02 0.0012482516 0.034319083
## lapse[11] 2.293325e-02 0.0004302561 0.020411655
## lapse[12] 8.809973e-03 0.0002173159 0.010745542
## lapse[13] 6.321151e-03 0.0001554539 0.008013144
## lapse[14] 1.754998e-01 0.0008847828 0.042063514
## lapse[15] 3.162915e-02 0.0009188842 0.030596757
## lapse[16] 7.148945e-03 0.0001741962 0.009202111
## lapse[17] 1.144275e-02 0.0002954621 0.013292900
## lapse[18] 6.627415e-03 0.0001744247 0.008371803
## lapse[19] 3.055945e-01 0.0008889376 0.042942279
## lapse[20] 8.371378e-03 0.0002613983 0.011426465
## lapse[21] 1.388446e-02 0.0003888759 0.017208503
## lapse[22] 7.519963e-03 0.0002068384 0.009602896
## lapse[23] 1.373136e-02 0.0003625989 0.016923914
## lapse[24] 3.789663e-01 0.0010057960 0.046255875
## lapse[25] 3.470031e-02 0.0007521844 0.030445742
## lapse[26] 4.321070e-02 0.0009021553 0.032605723
## lapse[27] 7.307764e-03 0.0001914448 0.009715021
## lapse[28] 1.769405e-02 0.0004841276 0.020153971
## lapse[29] 1.012011e-02 0.0003278112 0.014180895
## lapse[30] 9.235608e-02 0.0016664577 0.042297674
## lapse[31] 6.529406e-03 0.0001860562 0.008492468
## lapse[32] 1.037651e-01 0.0011177165 0.041229721
## lapse[33] 9.581101e-03 0.0002426445 0.012373254
## lapse[34] 1.070218e-02 0.0002565016 0.013041554
## lapse[35] 1.036222e-02 0.0002689875 0.012957962
## lapse[36] 7.504837e-03 0.0002062819 0.010247430
## lapse[37] 1.227706e-01 0.0011202013 0.043982364
## lapse[38] 9.794841e-03 0.0002454580 0.013364867
## lapse[39] 1.000240e-02 0.0002506846 0.011540652
## lapse[40] 5.639213e-03 0.0001349139 0.007005527
## lapse[41] 1.834837e-02 0.0004398243 0.018559752
## lapse[42] 2.065042e-01 0.0008609341 0.045929588
## lapse[43] 4.367270e-02 0.0008552371 0.032603603
## lapse[44] 7.865406e-03 0.0002249900 0.010954993
## lapse[45] 8.853747e-03 0.0002485478 0.011014157
## lapse[46] 3.609870e-01 0.0010813155 0.046227752
## lapse[47] 6.120091e-03 0.0001712874 0.007552938
## lapse[48] 7.082311e-03 0.0001927965 0.009459169
## lapse[49] 6.308862e-03 0.0002125960 0.008739449
## lapse[50] 2.017000e-01 0.0009234542 0.044863704
## lapse[51] 1.849332e-02 0.0005160492 0.021260547
## lapse[52] 1.551677e-02 0.0004357424 0.018597621
## lapse[53] 9.131947e-03 0.0002198237 0.011197217
## lapse[54] 1.109254e-02 0.0002885988 0.013514307
## lapse[55] 8.526205e-03 0.0002600209 0.011378778
## lapse[56] 5.750471e-03 0.0001495789 0.007353544
## lapse[57] 6.981577e-03 0.0001966539 0.009605325
## lapse[58] 8.740074e-03 0.0002528465 0.011218734
## lapse[59] 1.530800e-02 0.0004249029 0.018641142
## lapse[60] 3.534432e-02 0.0007472414 0.029477162
## lapse[61] 1.196786e-02 0.0003109995 0.015069620
## lapse[62] 1.964342e-02 0.0003744254 0.018253669
## lapse[63] 2.112580e-02 0.0005782310 0.022990473
## lapse[64] 2.810803e-02 0.0006798942 0.027219206
## lapse[65] 8.780729e-03 0.0002578739 0.011703278
## lapse[66] 1.969246e-02 0.0005265232 0.021924918
## lapse[67] 6.238877e-03 0.0001975248 0.008690480
## lapse[68] 5.049241e-02 0.0008748256 0.030328247
## lapse[69] 5.039659e-03 0.0001369375 0.006435998
## lapse[70] 9.359403e-03 0.0002343939 0.011473667
## lapse[71] 2.341653e-02 0.0005840420 0.023677875
## lapse[72] 1.984329e-01 0.0009317573 0.043500750
## lapse[73] 2.105327e-02 0.0004462982 0.020031496
## lapse[74] 7.742780e-03 0.0002178529 0.010266772
## lapse[75] 9.378440e-03 0.0002773536 0.013076990
## lapse[76] 2.386760e-02 0.0005140960 0.021477277
## lapse[77] 4.629438e-03 0.0001257736 0.006176479
## lapse[78] 6.757980e-03 0.0001895854 0.009023840
## lapse[79] 9.681566e-03 0.0002385657 0.012059080
## lapse[80] 3.275190e-02 0.0006280892 0.026799233
## lapse[81] 1.781770e-02 0.0003295492 0.017650472
## lapse[82] 1.458904e-02 0.0003908843 0.017586692
## lapse[83] 7.295156e-03 0.0002244153 0.009885037
## lapse[84] 6.444312e-03 0.0001627893 0.008210979
## lapse[85] 5.283590e-03 0.0001316903 0.006770891
## lapse[86] 8.356872e-02 0.0010332820 0.037913854
## lapse[87] 7.440426e-02 0.0013845566 0.038518571
## lapse[88] 1.231216e-02 0.0003439860 0.015431894
## lapse[89] 3.639981e-02 0.0006884703 0.028336768
## lapse[90] 2.328758e-02 0.0007346851 0.026002497
## lapse[91] 6.099569e-03 0.0001672222 0.008139306
## lapse[92] 1.472981e-02 0.0003886254 0.017001139
## lapse[93] 4.739123e-02 0.0009024975 0.032080249
## lapse[94] 2.027777e-01 0.0009380324 0.043785555
## lapse[95] 8.542762e-03 0.0002624306 0.011792612
## lapse[96] 8.506611e-02 0.0012731594 0.036081096
## lapse[97] 3.030348e-01 0.0009698645 0.046913236
## lapse[98] 6.784295e-03 0.0002017056 0.008982260
## lapse[99] 1.713316e-02 0.0004715324 0.020535914
## lapse[100] 9.299226e-03 0.0002386217 0.012306160
## lapse[101] 4.041922e-02 0.0010224394 0.034738623
## lapse[102] 7.111443e-03 0.0002027573 0.009904794
## lapse[103] 2.050665e-01 0.0008281701 0.040848956
## lapse[104] 1.104605e-02 0.0002566533 0.013445681
## lapse[105] 1.097801e-02 0.0002879890 0.013473719
## lapse[106] 2.738182e-02 0.0006353847 0.025709937
## lapse[107] 1.811439e-02 0.0005479753 0.023767281
## lapse[108] 9.824564e-03 0.0002481667 0.011871096
## lapse[109] 7.669447e-03 0.0002311331 0.010579096
## lapse[110] 1.177573e-01 0.0016633855 0.047526821
## lapse[111] 7.338701e-03 0.0002250038 0.010526665
## lapse[112] 9.408502e-03 0.0002454261 0.012002690
## lapse[113] 8.186379e-03 0.0002121183 0.010544514
## lapse[114] 7.947978e-02 0.0011989795 0.038725066
## lapse[115] 6.690230e-03 0.0001899519 0.008966253
## lapse[116] 7.627162e-03 0.0002383904 0.010763663
## lapse[117] 2.561959e-02 0.0004583829 0.023668928
## lapse[118] 1.295085e-01 0.0009947477 0.040151958
## lapse[119] 8.902239e-03 0.0002235097 0.011139361
## lapse[120] 8.535332e-03 0.0002485098 0.011615307
## lapse[121] 8.019031e-03 0.0002079438 0.010019130
## lapse[122] 6.444005e-03 0.0001883400 0.008531862
## lapse[123] 7.428270e-03 0.0002205401 0.010025461
## lapse[124] 8.955033e-03 0.0002606266 0.012111220
## lapse[125] 9.047081e-03 0.0002907492 0.012345764
## lapse[126] 3.499723e-02 0.0007117714 0.027985788
## lapse[127] 2.232456e-02 0.0005452520 0.023506166
## lapse[128] 1.366621e-01 0.0009786660 0.039035886
## lapse[129] 5.454611e-03 0.0001768542 0.007302139
## lapse[130] 1.832076e-02 0.0004447802 0.020991750
## lapse[131] 7.678065e-03 0.0001866727 0.009531340
## lapse[132] 6.322287e-02 0.0011074637 0.037139347
## lapse[133] 8.719855e-03 0.0002477582 0.011065518
## lapse[134] 1.007308e-02 0.0003390546 0.014246024
## lapse[135] 3.333293e-01 0.0009421343 0.044789263
## lapse[136] 1.181609e-02 0.0003592481 0.016156637
## lapse[137] 8.037018e-03 0.0001877219 0.010005456
## lapse[138] 9.070338e-03 0.0002601781 0.012062967
## lapse[139] 1.097218e-02 0.0003524057 0.014722776
## lapse[140] 6.357707e-03 0.0001900456 0.008853039
## lapse[141] 1.855167e-02 0.0004939012 0.021400195
## lapse[142] 4.130045e-02 0.0006662657 0.027758051
## lapse[143] 6.826410e-03 0.0001925439 0.009337732
## lapse[144] 2.010988e-02 0.0004258362 0.021324879
## lapse[145] 6.142936e-02 0.0010315042 0.035149798
## lapse[146] 3.150939e-02 0.0006206761 0.025397274
## lapse[147] 5.978181e-03 0.0001501429 0.007551552
## lapse[148] 4.380102e-02 0.0006795669 0.030709752
## lapse[149] 7.192731e-03 0.0001893868 0.009494871
## lapse[150] 6.497641e-03 0.0001886289 0.008575138
## lp__ -6.486936e+03 0.7747091211 18.379509918
## 2.5% 25% 50%
## sigma_log_threshold 9.345159e-03 6.997544e-02 1.124728e-01
## sigma_log_spread 1.449195e-01 2.199796e-01 2.599721e-01
## sigma_logit_lapse 1.542124e+00 1.807051e+00 1.958691e+00
## b_threshold[1] 8.296452e-01 9.046432e-01 9.404361e-01
## b_threshold[2] 7.572449e-01 8.323873e-01 8.705259e-01
## b_threshold[3] 7.265100e-01 8.143417e-01 8.587384e-01
## b_spread[1] 2.853101e-01 3.905803e-01 4.440814e-01
## b_spread[2] 3.058491e-01 4.205023e-01 4.729769e-01
## b_spread[3] 4.214857e-01 5.384892e-01 5.987782e-01
## b_lapse[1] -5.556520e+00 -4.924277e+00 -4.593624e+00
## b_lapse[2] -5.753747e+00 -5.102776e+00 -4.760292e+00
## b_lapse[3] -5.334279e+00 -4.639188e+00 -4.296776e+00
## threshold_zoffset[1] -1.878880e+00 -5.075408e-01 1.193398e-01
## threshold_zoffset[2] -1.708489e+00 -5.182429e-01 1.645747e-01
## threshold_zoffset[3] -1.916782e+00 -6.934494e-01 -9.572805e-02
## threshold_zoffset[4] -1.726455e+00 -5.274195e-01 6.656716e-02
## threshold_zoffset[5] -1.852355e+00 -6.814094e-01 1.940578e-03
## threshold_zoffset[6] -2.062390e+00 -9.750322e-01 -3.902131e-01
## threshold_zoffset[7] -1.702814e+00 -4.382420e-01 2.756759e-01
## threshold_zoffset[8] -2.035694e+00 -7.778991e-01 -1.247072e-01
## threshold_zoffset[9] -2.059711e+00 -9.905024e-01 -4.399414e-01
## threshold_zoffset[10] -1.976618e+00 -6.449796e-01 3.027261e-03
## threshold_zoffset[11] -1.845575e+00 -6.186047e-01 8.343348e-03
## threshold_zoffset[12] -1.911539e+00 -5.682394e-01 3.366213e-02
## threshold_zoffset[13] -1.924421e+00 -6.745216e-01 -6.334274e-02
## threshold_zoffset[14] -2.057760e+00 -7.318096e-01 -8.401600e-02
## threshold_zoffset[15] -1.609274e+00 -2.898319e-01 3.906173e-01
## threshold_zoffset[16] -2.051082e+00 -8.548644e-01 -2.527533e-01
## threshold_zoffset[17] -1.933066e+00 -8.063829e-01 -1.982142e-01
## threshold_zoffset[18] -2.366925e+00 -1.183309e+00 -5.685132e-01
## threshold_zoffset[19] -1.950763e+00 -6.693299e-01 9.557828e-03
## threshold_zoffset[20] -1.878878e+00 -6.355707e-01 -1.923898e-02
## threshold_zoffset[21] -1.772896e+00 -5.268882e-01 1.512694e-01
## threshold_zoffset[22] -1.956660e+00 -8.337116e-01 -1.844299e-01
## threshold_zoffset[23] -1.671281e+00 -3.269621e-01 3.247135e-01
## threshold_zoffset[24] -1.971195e+00 -7.058765e-01 -1.574602e-02
## threshold_zoffset[25] -1.646303e+00 -2.138007e-01 4.674952e-01
## threshold_zoffset[26] -1.839026e+00 -5.163806e-01 1.905228e-01
## threshold_zoffset[27] -1.763951e+00 -4.433642e-01 1.864171e-01
## threshold_zoffset[28] -1.867459e+00 -3.686068e-01 2.740849e-01
## threshold_zoffset[29] -1.471687e+00 -7.008750e-02 6.230516e-01
## threshold_zoffset[30] -1.734297e+00 -4.537162e-01 2.520766e-01
## threshold_zoffset[31] -2.008828e+00 -8.284830e-01 -2.186309e-01
## threshold_zoffset[32] -1.886789e+00 -5.560266e-01 1.821282e-01
## threshold_zoffset[33] -2.183740e+00 -9.878920e-01 -3.445130e-01
## threshold_zoffset[34] -1.886210e+00 -6.563621e-01 -4.544149e-02
## threshold_zoffset[35] -1.731795e+00 -4.804514e-01 1.384049e-01
## threshold_zoffset[36] -2.266887e+00 -1.033383e+00 -3.905433e-01
## threshold_zoffset[37] -1.860717e+00 -5.957015e-01 7.831360e-02
## threshold_zoffset[38] -1.667246e+00 -4.479032e-01 1.947063e-01
## threshold_zoffset[39] -2.263684e+00 -1.064661e+00 -4.433362e-01
## threshold_zoffset[40] -2.207947e+00 -1.133350e+00 -5.438318e-01
## threshold_zoffset[41] -1.802022e+00 -5.906091e-01 2.209821e-02
## threshold_zoffset[42] -1.738927e+00 -5.200511e-01 1.513002e-01
## threshold_zoffset[43] -1.745234e+00 -4.295765e-01 2.246457e-01
## threshold_zoffset[44] -2.056851e+00 -8.662544e-01 -2.458666e-01
## threshold_zoffset[45] -1.962131e+00 -7.373919e-01 -1.152092e-01
## threshold_zoffset[46] -1.888426e+00 -6.806622e-01 -2.022123e-02
## threshold_zoffset[47] -2.498163e+00 -1.229500e+00 -6.167522e-01
## threshold_zoffset[48] -2.358254e+00 -1.154125e+00 -5.929280e-01
## threshold_zoffset[49] -2.306810e+00 -1.189126e+00 -6.064364e-01
## threshold_zoffset[50] -1.915379e+00 -5.688389e-01 1.444679e-01
## threshold_zoffset[51] -2.032154e+00 -6.909076e-01 2.984455e-02
## threshold_zoffset[52] -1.762496e+00 -4.110789e-01 2.901394e-01
## threshold_zoffset[53] -2.130154e+00 -1.113475e+00 -4.821745e-01
## threshold_zoffset[54] -1.636029e+00 -3.447828e-01 2.644040e-01
## threshold_zoffset[55] -1.552147e+00 -3.011367e-01 3.278161e-01
## threshold_zoffset[56] -2.050740e+00 -9.639186e-01 -3.398148e-01
## threshold_zoffset[57] -2.257709e+00 -1.114644e+00 -4.896425e-01
## threshold_zoffset[58] -1.523286e+00 -3.411899e-01 2.634506e-01
## threshold_zoffset[59] -1.565768e+00 -1.700894e-01 5.444971e-01
## threshold_zoffset[60] -1.587885e+00 -2.967436e-01 3.632840e-01
## threshold_zoffset[61] -1.583667e+00 -2.858357e-01 3.711181e-01
## threshold_zoffset[62] -1.955492e+00 -7.146021e-01 -4.199558e-02
## threshold_zoffset[63] -1.803827e+00 -4.504142e-01 2.056653e-01
## threshold_zoffset[64] -1.544310e+00 -2.670915e-01 3.391061e-01
## threshold_zoffset[65] -2.033197e+00 -8.654735e-01 -2.526567e-01
## threshold_zoffset[66] -1.480078e+00 -1.850036e-01 5.497972e-01
## threshold_zoffset[67] -2.216791e+00 -1.031887e+00 -4.503107e-01
## threshold_zoffset[68] -1.794525e+00 -3.994518e-01 2.767221e-01
## threshold_zoffset[69] -2.211188e+00 -1.004092e+00 -4.114998e-01
## threshold_zoffset[70] -2.306136e+00 -1.207444e+00 -5.731874e-01
## threshold_zoffset[71] -1.820448e+00 -5.728207e-01 2.772788e-02
## threshold_zoffset[72] -1.815657e+00 -4.507344e-01 2.019319e-01
## threshold_zoffset[73] -1.721047e+00 -5.326936e-01 1.040154e-01
## threshold_zoffset[74] -1.768837e+00 -6.789911e-01 -1.100326e-01
## threshold_zoffset[75] -1.763004e+00 -4.484043e-01 2.266533e-01
## threshold_zoffset[76] -2.016150e+00 -6.801283e-01 -6.871029e-02
## threshold_zoffset[77] -2.582437e+00 -1.443212e+00 -9.054538e-01
## threshold_zoffset[78] -1.739612e+00 -5.282352e-01 1.091340e-01
## threshold_zoffset[79] -2.262142e+00 -1.161268e+00 -5.596833e-01
## threshold_zoffset[80] -1.661616e+00 -3.884564e-01 2.953051e-01
## threshold_zoffset[81] -2.165996e+00 -9.962732e-01 -3.149969e-01
## threshold_zoffset[82] -1.569906e+00 -4.324985e-01 3.057706e-01
## threshold_zoffset[83] -1.618982e+00 -3.831178e-01 2.395425e-01
## threshold_zoffset[84] -1.813004e+00 -7.404016e-01 -1.610395e-01
## threshold_zoffset[85] -2.133881e+00 -9.650944e-01 -4.211729e-01
## threshold_zoffset[86] -1.802553e+00 -5.968744e-01 6.315612e-02
## threshold_zoffset[87] -1.874355e+00 -5.383753e-01 1.463211e-01
## threshold_zoffset[88] -1.536699e+00 -3.801724e-01 2.061196e-01
## threshold_zoffset[89] -1.678687e+00 -4.316226e-01 2.459519e-01
## threshold_zoffset[90] -1.593532e+00 -2.304349e-01 5.277836e-01
## threshold_zoffset[91] -2.333794e+00 -1.096176e+00 -4.853527e-01
## threshold_zoffset[92] -1.815840e+00 -4.082546e-01 3.284505e-01
## threshold_zoffset[93] -1.921682e+00 -5.975776e-01 4.197965e-02
## threshold_zoffset[94] -1.934139e+00 -6.276730e-01 7.801492e-02
## threshold_zoffset[95] -1.844373e+00 -5.553345e-01 5.463584e-02
## threshold_zoffset[96] -2.073165e+00 -8.456887e-01 -1.601701e-01
## threshold_zoffset[97] -2.048098e+00 -7.871722e-01 -1.162461e-01
## threshold_zoffset[98] -2.277701e+00 -1.182605e+00 -5.550153e-01
## threshold_zoffset[99] -1.670114e+00 -3.645963e-01 2.745170e-01
## threshold_zoffset[100] -1.871386e+00 -5.038787e-01 1.233054e-01
## threshold_zoffset[101] -1.918928e+00 -6.093423e-01 8.398210e-02
## threshold_zoffset[102] -2.090134e+00 -8.111996e-01 -2.122709e-01
## threshold_zoffset[103] -1.875119e+00 -6.117731e-01 4.433453e-02
## threshold_zoffset[104] -2.110181e+00 -8.475776e-01 -2.794020e-01
## threshold_zoffset[105] -1.773802e+00 -6.357270e-01 -8.221817e-02
## threshold_zoffset[106] -1.737210e+00 -4.650662e-01 1.958012e-01
## threshold_zoffset[107] -1.163000e+00 3.479932e-01 1.165113e+00
## threshold_zoffset[108] -2.029189e+00 -8.809009e-01 -1.482114e-01
## threshold_zoffset[109] -1.876701e+00 -7.138234e-01 -4.531518e-02
## threshold_zoffset[110] -1.790718e+00 -4.087820e-01 2.052580e-01
## threshold_zoffset[111] -1.777483e+00 -5.288800e-01 1.332083e-01
## threshold_zoffset[112] -1.744092e+00 -5.431092e-01 6.281307e-02
## threshold_zoffset[113] -2.184777e+00 -9.407391e-01 -3.145631e-01
## threshold_zoffset[114] -1.950683e+00 -7.332463e-01 -7.916546e-02
## threshold_zoffset[115] -2.072062e+00 -9.049790e-01 -2.700706e-01
## threshold_zoffset[116] -1.675374e+00 -6.023859e-01 3.605190e-02
## threshold_zoffset[117] -1.589214e+00 -3.675170e-01 2.756592e-01
## threshold_zoffset[118] -1.854926e+00 -5.640078e-01 8.961580e-02
## threshold_zoffset[119] -1.552068e+00 -2.911466e-01 3.707920e-01
## threshold_zoffset[120] -1.945483e+00 -6.340317e-01 9.416666e-04
## threshold_zoffset[121] -1.756288e+00 -5.355873e-01 8.457756e-02
## threshold_zoffset[122] -1.781241e+00 -6.700736e-01 -9.590645e-02
## threshold_zoffset[123] -1.983073e+00 -6.573291e-01 -2.442498e-02
## threshold_zoffset[124] -1.582238e+00 -3.479265e-01 3.273912e-01
## threshold_zoffset[125] -1.585477e+00 -3.242609e-01 3.486562e-01
## threshold_zoffset[126] -1.805640e+00 -3.994751e-01 2.248738e-01
## threshold_zoffset[127] -1.529567e+00 -2.774501e-01 3.987489e-01
## threshold_zoffset[128] -2.132627e+00 -7.660845e-01 -9.545843e-02
## threshold_zoffset[129] -2.220936e+00 -1.118236e+00 -5.274382e-01
## threshold_zoffset[130] -1.766432e+00 -3.329036e-01 3.163781e-01
## threshold_zoffset[131] -1.826409e+00 -6.121958e-01 -2.289991e-02
## threshold_zoffset[132] -1.695965e+00 -4.359935e-01 2.422140e-01
## threshold_zoffset[133] -1.951500e+00 -7.791335e-01 -1.165353e-01
## threshold_zoffset[134] -1.632425e+00 -3.705372e-01 3.073783e-01
## threshold_zoffset[135] -1.958542e+00 -6.800513e-01 3.472242e-03
## threshold_zoffset[136] -1.654614e+00 -3.605292e-01 3.317950e-01
## threshold_zoffset[137] -1.904785e+00 -7.457253e-01 -1.048895e-01
## threshold_zoffset[138] -1.695213e+00 -3.963623e-01 2.332885e-01
## threshold_zoffset[139] -1.572385e+00 -2.066143e-01 4.660529e-01
## threshold_zoffset[140] -2.099452e+00 -7.896315e-01 -1.266033e-01
## threshold_zoffset[141] -1.862407e+00 -6.057912e-01 3.513842e-02
## threshold_zoffset[142] -1.628328e+00 -4.344323e-01 1.977933e-01
## threshold_zoffset[143] -1.685729e+00 -4.094691e-01 1.719143e-01
## threshold_zoffset[144] -1.775966e+00 -4.146448e-01 2.189406e-01
## threshold_zoffset[145] -1.743203e+00 -6.396144e-01 1.785030e-02
## threshold_zoffset[146] -1.723018e+00 -3.192522e-01 2.932881e-01
## threshold_zoffset[147] -2.744077e+00 -1.602360e+00 -9.652046e-01
## threshold_zoffset[148] -1.716098e+00 -5.431293e-01 1.052742e-01
## threshold_zoffset[149] -2.227762e+00 -9.949480e-01 -3.919055e-01
## threshold_zoffset[150] -1.925711e+00 -7.756488e-01 -1.365999e-01
## spread_zoffset[1] -1.600438e+00 -3.120441e-01 3.944383e-01
## spread_zoffset[2] -1.352400e+00 -7.217208e-02 4.988869e-01
## spread_zoffset[3] -1.559659e+00 -4.719100e-01 1.147224e-01
## spread_zoffset[4] -9.967571e-01 1.392426e-01 6.498129e-01
## spread_zoffset[5] -1.403317e+00 -1.977776e-01 4.578850e-01
## spread_zoffset[6] -2.343250e+00 -1.275434e+00 -7.762522e-01
## spread_zoffset[7] -1.067730e+00 -3.140386e-02 5.152684e-01
## spread_zoffset[8] -1.697085e+00 -2.380862e-01 5.039576e-01
## spread_zoffset[9] -2.355580e+00 -1.395510e+00 -8.639824e-01
## spread_zoffset[10] -1.265952e+00 -1.880655e-02 7.181359e-01
## spread_zoffset[11] -1.880227e+00 -7.027203e-01 -5.597234e-02
## spread_zoffset[12] -2.024507e+00 -9.441322e-01 -4.188050e-01
## spread_zoffset[13] -2.063770e+00 -9.925336e-01 -4.612663e-01
## spread_zoffset[14] -2.052142e+00 -7.656956e-01 -6.256879e-02
## spread_zoffset[15] -1.328185e+00 -3.808782e-03 6.658964e-01
## spread_zoffset[16] -2.244065e+00 -1.312657e+00 -7.902450e-01
## spread_zoffset[17] -1.782219e+00 -4.864712e-01 1.241268e-01
## spread_zoffset[18] -2.131126e+00 -1.084975e+00 -5.542284e-01
## spread_zoffset[19] -1.909417e+00 -6.529305e-01 -8.264337e-03
## spread_zoffset[20] -1.463089e+00 -4.661116e-01 1.089585e-02
## spread_zoffset[21] -1.069111e+00 -4.443236e-02 4.523688e-01
## spread_zoffset[22] -1.699507e+00 -7.589831e-01 -2.747160e-01
## spread_zoffset[23] -1.354343e+00 -2.303138e-01 2.919527e-01
## spread_zoffset[24] -1.854429e+00 -6.771602e-01 1.650381e-02
## spread_zoffset[25] -1.184150e+00 1.331083e-01 7.522226e-01
## spread_zoffset[26] -1.691024e+00 -4.305071e-01 3.190390e-01
## spread_zoffset[27] -1.560558e+00 -6.980840e-01 -2.373268e-01
## spread_zoffset[28] -1.113422e+00 1.872928e-02 5.752602e-01
## spread_zoffset[29] -1.261441e+00 -2.696479e-01 2.167093e-01
## spread_zoffset[30] -1.607354e+00 -3.477843e-01 3.171108e-01
## spread_zoffset[31] -2.082068e+00 -1.051229e+00 -4.851295e-01
## spread_zoffset[32] -1.688016e+00 -4.223316e-01 2.966133e-01
## spread_zoffset[33] -1.074820e+00 -8.067176e-02 4.033031e-01
## spread_zoffset[34] -1.528616e+00 -4.238745e-01 8.857943e-02
## spread_zoffset[35] -1.855325e+00 -5.782455e-01 -6.301893e-02
## spread_zoffset[36] -1.612408e+00 -6.410866e-01 -9.238596e-02
## spread_zoffset[37] -1.549790e+00 -3.232499e-01 4.069268e-01
## spread_zoffset[38] -1.270230e+00 -2.609999e-01 1.919982e-01
## spread_zoffset[39] -1.464161e+00 -4.218463e-01 1.114522e-01
## spread_zoffset[40] -2.185522e+00 -1.221124e+00 -7.221882e-01
## spread_zoffset[41] -1.971508e+00 -6.815891e-01 -4.068841e-02
## spread_zoffset[42] -1.654220e+00 -4.542602e-01 1.965348e-01
## spread_zoffset[43] -1.719444e+00 -3.746091e-01 4.079358e-01
## spread_zoffset[44] -1.583265e+00 -6.576503e-01 -1.221652e-01
## spread_zoffset[45] -1.946546e+00 -9.498358e-01 -3.877569e-01
## spread_zoffset[46] -1.978046e+00 -7.274417e-01 -4.055707e-02
## spread_zoffset[47] -2.771230e+00 -1.714753e+00 -1.205897e+00
## spread_zoffset[48] -1.902099e+00 -8.762321e-01 -3.446854e-01
## spread_zoffset[49] -2.120696e+00 -1.127083e+00 -5.699554e-01
## spread_zoffset[50] -1.624528e+00 -2.018752e-01 4.408874e-01
## spread_zoffset[51] -1.350699e+00 1.455517e-03 5.792093e-01
## spread_zoffset[52] -9.103730e-01 2.128993e-01 7.139909e-01
## spread_zoffset[53] -2.435742e+00 -1.302621e+00 -7.109826e-01
## spread_zoffset[54] -1.788913e+00 -7.310300e-01 -1.844778e-01
## spread_zoffset[55] -1.453687e+00 -4.993017e-01 -3.723558e-03
## spread_zoffset[56] -2.453974e+00 -1.366697e+00 -8.103181e-01
## spread_zoffset[57] -2.204241e+00 -1.177010e+00 -6.608635e-01
## spread_zoffset[58] -2.228810e+00 -1.177459e+00 -6.769249e-01
## spread_zoffset[59] -9.892703e-01 5.312419e-02 5.414645e-01
## spread_zoffset[60] -1.416163e+00 -2.037816e-01 4.363338e-01
## spread_zoffset[61] -1.161152e+00 -1.820121e-01 2.846506e-01
## spread_zoffset[62] -2.294311e+00 -1.070899e+00 -3.917341e-01
## spread_zoffset[63] -1.221456e+00 2.261715e-02 5.649820e-01
## spread_zoffset[64] -1.106331e+00 1.399765e-01 6.857045e-01
## spread_zoffset[65] -8.319342e-01 1.307272e-01 6.062973e-01
## spread_zoffset[66] -1.336926e+00 -1.545775e-01 3.604571e-01
## spread_zoffset[67] -2.173710e+00 -1.191532e+00 -6.553010e-01
## spread_zoffset[68] -1.849602e+00 -5.971617e-01 7.102430e-02
## spread_zoffset[69] -2.980006e+00 -1.909560e+00 -1.392474e+00
## spread_zoffset[70] -1.679015e+00 -5.312239e-01 3.823931e-02
## spread_zoffset[71] -1.265778e+00 -3.522191e-02 5.766536e-01
## spread_zoffset[72] -1.570277e+00 -3.037264e-01 3.655725e-01
## spread_zoffset[73] -1.713943e+00 -5.402286e-01 1.074320e-01
## spread_zoffset[74] -1.535629e+00 -5.109684e-01 -5.064556e-03
## spread_zoffset[75] -1.226541e+00 -1.905640e-01 2.614497e-01
## spread_zoffset[76] -1.841142e+00 -6.517596e-01 3.946764e-02
## spread_zoffset[77] -3.282803e+00 -2.264001e+00 -1.710914e+00
## spread_zoffset[78] -1.807822e+00 -8.669614e-01 -3.732862e-01
## spread_zoffset[79] -1.464317e+00 -2.819258e-01 2.405909e-01
## spread_zoffset[80] -1.620246e+00 -3.934740e-01 2.870601e-01
## spread_zoffset[81] -1.562150e+00 -4.842827e-01 1.293609e-01
## spread_zoffset[82] -1.068681e+00 -4.005915e-02 4.927577e-01
## spread_zoffset[83] -1.731395e+00 -6.962759e-01 -1.935349e-01
## spread_zoffset[84] -2.510695e+00 -1.497553e+00 -9.360307e-01
## spread_zoffset[85] -2.582175e+00 -1.599470e+00 -1.038390e+00
## spread_zoffset[86] -2.103105e+00 -1.018827e+00 -3.843474e-01
## spread_zoffset[87] -1.918755e+00 -5.642080e-01 2.052556e-01
## spread_zoffset[88] -1.184982e+00 -1.866933e-01 3.530417e-01
## spread_zoffset[89] -1.500176e+00 -2.702998e-01 4.137541e-01
## spread_zoffset[90] -7.996866e-01 4.298372e-01 9.838305e-01
## spread_zoffset[91] -2.215255e+00 -1.180261e+00 -6.887798e-01
## spread_zoffset[92] -1.205123e+00 -1.804212e-01 3.167018e-01
## spread_zoffset[93] -1.626526e+00 -2.941670e-01 3.796418e-01
## spread_zoffset[94] -1.945212e+00 -6.379477e-01 4.499975e-02
## spread_zoffset[95] -1.367083e+00 -2.407748e-01 2.422460e-01
## spread_zoffset[96] -1.944161e+00 -7.416366e-01 4.622970e-02
## spread_zoffset[97] -1.910383e+00 -5.689295e-01 1.570583e-01
## spread_zoffset[98] -2.670438e+00 -1.516404e+00 -9.835310e-01
## spread_zoffset[99] -1.043086e+00 1.127762e-01 6.421574e-01
## spread_zoffset[100] -1.146561e+00 -1.812428e-01 3.097533e-01
## spread_zoffset[101] -1.040624e+00 3.893106e-01 1.049285e+00
## spread_zoffset[102] -1.780139e+00 -8.330894e-01 -3.118091e-01
## spread_zoffset[103] -1.867026e+00 -5.130332e-01 1.522942e-01
## spread_zoffset[104] -1.902956e+00 -7.261792e-01 -1.870527e-01
## spread_zoffset[105] -1.672230e+00 -5.011030e-01 4.314446e-02
## spread_zoffset[106] -1.265042e+00 -4.822983e-02 5.255871e-01
## spread_zoffset[107] -1.067358e+00 2.284957e-01 8.012334e-01
## spread_zoffset[108] -1.504725e+00 -4.435901e-01 6.237506e-02
## spread_zoffset[109] -1.569876e+00 -5.179925e-01 -4.052531e-02
## spread_zoffset[110] -1.575505e+00 -2.463712e-01 4.630994e-01
## spread_zoffset[111] -1.708353e+00 -7.662495e-01 -2.770350e-01
## spread_zoffset[112] -1.754274e+00 -7.556108e-01 -2.383742e-01
## spread_zoffset[113] -2.022286e+00 -9.474264e-01 -4.598632e-01
## spread_zoffset[114] -1.705470e+00 -4.206187e-01 3.076868e-01
## spread_zoffset[115] -1.556766e+00 -5.907640e-01 -4.560582e-02
## spread_zoffset[116] -1.799397e+00 -8.022584e-01 -2.845363e-01
## spread_zoffset[117] -1.512260e+00 -2.601533e-01 3.207615e-01
## spread_zoffset[118] -1.820345e+00 -4.868986e-01 2.464842e-01
## spread_zoffset[119] -1.892594e+00 -8.096767e-01 -3.295424e-01
## spread_zoffset[120] -8.718151e-01 1.774670e-01 6.341603e-01
## spread_zoffset[121] -1.807458e+00 -7.714093e-01 -2.815942e-01
## spread_zoffset[122] -2.211284e+00 -1.280492e+00 -8.066146e-01
## spread_zoffset[123] -1.738539e+00 -7.701856e-01 -2.929604e-01
## spread_zoffset[124] -1.080208e+00 -1.598150e-01 3.111001e-01
## spread_zoffset[125] -1.412982e+00 -4.477881e-01 -3.664086e-04
## spread_zoffset[126] -1.734154e+00 -4.184829e-01 2.807407e-01
## spread_zoffset[127] -1.261221e+00 1.317099e-01 6.787870e-01
## spread_zoffset[128] -2.178610e+00 -9.088993e-01 -2.462598e-01
## spread_zoffset[129] -2.304121e+00 -1.250992e+00 -7.218011e-01
## spread_zoffset[130] -1.032508e+00 5.898734e-02 6.062227e-01
## spread_zoffset[131] -2.109862e+00 -1.106385e+00 -5.942605e-01
## spread_zoffset[132] -1.737000e+00 -3.381315e-01 3.739843e-01
## spread_zoffset[133] -1.950597e+00 -9.387781e-01 -4.127933e-01
## spread_zoffset[134] -1.192067e+00 -1.915981e-01 3.048137e-01
## spread_zoffset[135] -2.012128e+00 -7.570900e-01 -8.670911e-02
## spread_zoffset[136] -6.707478e-01 2.954952e-01 8.257395e-01
## spread_zoffset[137] -1.968401e+00 -9.370062e-01 -4.020266e-01
## spread_zoffset[138] -1.683348e+00 -6.363847e-01 -1.404250e-01
## spread_zoffset[139] -1.203235e+00 -1.666850e-01 3.256672e-01
## spread_zoffset[140] -2.103137e+00 -1.149324e+00 -6.133480e-01
## spread_zoffset[141] -1.348167e+00 -7.264292e-02 4.795102e-01
## spread_zoffset[142] -2.255675e+00 -9.990199e-01 -2.186061e-01
## spread_zoffset[143] -1.922142e+00 -9.441635e-01 -3.867895e-01
## spread_zoffset[144] -1.536280e+00 -3.688690e-01 1.821268e-01
## spread_zoffset[145] -1.830814e+00 -4.849875e-01 2.556775e-01
## spread_zoffset[146] -1.808532e+00 -5.074061e-01 1.393376e-01
## spread_zoffset[147] -3.082883e+00 -2.018515e+00 -1.436622e+00
## spread_zoffset[148] -1.675388e+00 -4.071748e-01 2.522456e-01
## spread_zoffset[149] -1.840379e+00 -9.235098e-01 -4.124913e-01
## spread_zoffset[150] -1.962223e+00 -9.756549e-01 -4.631290e-01
## lapse_zoffset[1] 3.947494e-01 1.018993e+00 1.234677e+00
## lapse_zoffset[2] -1.928159e+00 -6.226423e-01 6.043027e-02
## lapse_zoffset[3] -1.516462e+00 -2.469390e-01 2.023328e-01
## lapse_zoffset[4] -1.963552e+00 -9.046061e-01 -3.221304e-01
## lapse_zoffset[5] -1.576761e+00 -2.399173e-01 2.643812e-01
## lapse_zoffset[6] -2.153414e+00 -1.049639e+00 -5.097083e-01
## lapse_zoffset[7] -2.020907e+00 -6.927743e-01 -9.313259e-02
## lapse_zoffset[8] -1.382701e+00 2.229503e-01 5.908277e-01
## lapse_zoffset[9] -2.179793e+00 -1.106958e+00 -5.814113e-01
## lapse_zoffset[10] -1.337004e+00 4.295130e-01 8.234463e-01
## lapse_zoffset[11] -1.572011e+00 -1.260096e-01 3.703405e-01
## lapse_zoffset[12] -2.076611e+00 -1.035712e+00 -5.120796e-01
## lapse_zoffset[13] -2.098263e+00 -1.058876e+00 -5.638126e-01
## lapse_zoffset[14] 8.878914e-01 1.239414e+00 1.404919e+00
## lapse_zoffset[15] -1.623122e+00 -1.342425e-01 4.726802e-01
## lapse_zoffset[16] -2.316808e+00 -1.210124e+00 -6.522373e-01
## lapse_zoffset[17] -1.876627e+00 -7.187222e-01 -1.408152e-01
## lapse_zoffset[18] -2.066138e+00 -1.097985e+00 -5.310457e-01
## lapse_zoffset[19] 1.460254e+00 1.752474e+00 1.930255e+00
## lapse_zoffset[20] -2.184793e+00 -1.056677e+00 -4.700172e-01
## lapse_zoffset[21] -2.013153e+00 -8.645187e-01 -3.113070e-01
## lapse_zoffset[22] -2.230902e+00 -1.122020e+00 -6.237165e-01
## lapse_zoffset[23] -2.066728e+00 -7.030121e-01 -1.183650e-01
## lapse_zoffset[24] 1.617487e+00 1.922660e+00 2.106036e+00
## lapse_zoffset[25] -1.547887e+00 -5.410697e-02 5.199415e-01
## lapse_zoffset[26] -1.398061e+00 5.931798e-02 5.395164e-01
## lapse_zoffset[27] -2.170668e+00 -1.018580e+00 -4.860681e-01
## lapse_zoffset[28] -1.851977e+00 -5.921265e-01 2.666561e-02
## lapse_zoffset[29] -2.002639e+00 -9.073457e-01 -3.704453e-01
## lapse_zoffset[30] -4.682467e-01 7.803135e-01 1.027605e+00
## lapse_zoffset[31] -2.205932e+00 -1.046491e+00 -4.759601e-01
## lapse_zoffset[32] 2.618267e-01 1.020985e+00 1.234419e+00
## lapse_zoffset[33] -2.158409e+00 -9.191710e-01 -3.782117e-01
## lapse_zoffset[34] -2.054106e+00 -8.240851e-01 -2.739552e-01
## lapse_zoffset[35] -2.037757e+00 -8.894092e-01 -3.017795e-01
## lapse_zoffset[36] -2.097120e+00 -1.023898e+00 -4.607459e-01
## lapse_zoffset[37] 6.814237e-01 1.211979e+00 1.421899e+00
## lapse_zoffset[38] -2.180551e+00 -9.110376e-01 -3.124767e-01
## lapse_zoffset[39] -2.057644e+00 -9.417699e-01 -4.300731e-01
## lapse_zoffset[40] -2.112232e+00 -1.132994e+00 -6.210592e-01
## lapse_zoffset[41] -1.808357e+00 -4.679186e-01 9.649899e-02
## lapse_zoffset[42] 1.033788e+00 1.345813e+00 1.505074e+00
## lapse_zoffset[43] -1.359597e+00 3.477356e-01 7.698269e-01
## lapse_zoffset[44] -2.117141e+00 -9.842939e-01 -4.306773e-01
## lapse_zoffset[45] -2.129720e+00 -1.032252e+00 -5.262519e-01
## lapse_zoffset[46] 1.589227e+00 1.881958e+00 2.057492e+00
## lapse_zoffset[47] -2.252315e+00 -1.191544e+00 -7.263298e-01
## lapse_zoffset[48] -2.253460e+00 -1.097607e+00 -5.289168e-01
## lapse_zoffset[49] -2.260183e+00 -1.091813e+00 -6.013009e-01
## lapse_zoffset[50] 1.021644e+00 1.328413e+00 1.494408e+00
## lapse_zoffset[51] -2.008228e+00 -7.318750e-01 -1.427390e-01
## lapse_zoffset[52] -1.920016e+00 -7.070750e-01 -2.001278e-02
## lapse_zoffset[53] -2.163395e+00 -1.056759e+00 -5.082627e-01
## lapse_zoffset[54] -1.971647e+00 -9.485396e-01 -4.501817e-01
## lapse_zoffset[55] -2.180485e+00 -1.010601e+00 -4.469549e-01
## lapse_zoffset[56] -2.089770e+00 -1.111044e+00 -5.942683e-01
## lapse_zoffset[57] -2.317552e+00 -1.204555e+00 -6.677557e-01
## lapse_zoffset[58] -2.152277e+00 -1.112427e+00 -5.571719e-01
## lapse_zoffset[59] -2.080213e+00 -8.262245e-01 -2.571155e-01
## lapse_zoffset[60] -1.407093e+00 -1.054492e-01 3.895094e-01
## lapse_zoffset[61] -2.023417e+00 -9.241019e-01 -4.075161e-01
## lapse_zoffset[62] -1.583583e+00 -4.430497e-01 1.216241e-02
## lapse_zoffset[63] -1.730981e+00 -5.968408e-01 -2.632608e-02
## lapse_zoffset[64] -1.713615e+00 -3.435156e-01 1.933924e-01
## lapse_zoffset[65] -2.121395e+00 -9.788283e-01 -4.206519e-01
## lapse_zoffset[66] -1.939209e+00 -6.755746e-01 -6.147535e-02
## lapse_zoffset[67] -2.287809e+00 -1.163346e+00 -6.313017e-01
## lapse_zoffset[68] -9.446192e-01 5.133844e-01 8.109702e-01
## lapse_zoffset[69] -2.144672e+00 -1.083825e+00 -6.062011e-01
## lapse_zoffset[70] -2.018046e+00 -9.055559e-01 -3.596220e-01
## lapse_zoffset[71] -1.754256e+00 -3.608455e-01 2.209187e-01
## lapse_zoffset[72] 1.187883e+00 1.539258e+00 1.711990e+00
## lapse_zoffset[73] -1.706956e+00 -4.532124e-01 3.739087e-02
## lapse_zoffset[74] -2.076652e+00 -9.839801e-01 -4.624059e-01
## lapse_zoffset[75] -2.108384e+00 -9.758738e-01 -4.185347e-01
## lapse_zoffset[76] -1.546126e+00 -1.225972e-01 3.797846e-01
## lapse_zoffset[77] -2.175246e+00 -1.177843e+00 -6.526346e-01
## lapse_zoffset[78] -2.124585e+00 -1.016972e+00 -4.781291e-01
## lapse_zoffset[79] -2.038678e+00 -9.276115e-01 -3.591445e-01
## lapse_zoffset[80] -1.419040e+00 -1.270005e-01 3.555674e-01
## lapse_zoffset[81] -1.770500e+00 -5.373276e-01 -5.770115e-02
## lapse_zoffset[82] -2.124373e+00 -7.305598e-01 -1.269669e-01
## lapse_zoffset[83] -2.100695e+00 -1.033676e+00 -5.046524e-01
## lapse_zoffset[84] -2.126973e+00 -1.109428e+00 -5.678436e-01
## lapse_zoffset[85] -2.246265e+00 -1.085210e+00 -5.786974e-01
## lapse_zoffset[86] 1.924947e-02 7.281317e-01 9.530622e-01
## lapse_zoffset[87] -4.619047e-01 8.454791e-01 1.118235e+00
## lapse_zoffset[88] -1.993808e+00 -8.343840e-01 -2.479401e-01
## lapse_zoffset[89] -1.193325e+00 1.450673e-01 5.677912e-01
## lapse_zoffset[90] -1.837223e+00 -4.575584e-01 2.078601e-01
## lapse_zoffset[91] -2.317258e+00 -1.103327e+00 -5.373266e-01
## lapse_zoffset[92] -1.994267e+00 -8.388009e-01 -2.682042e-01
## lapse_zoffset[93] -1.151278e+00 4.916556e-01 8.215239e-01
## lapse_zoffset[94] 1.011485e+00 1.342421e+00 1.504212e+00
## lapse_zoffset[95] -2.154236e+00 -9.497847e-01 -4.061781e-01
## lapse_zoffset[96] 1.155625e-01 9.816500e-01 1.196107e+00
## lapse_zoffset[97] 1.456669e+00 1.748449e+00 1.923443e+00
## lapse_zoffset[98] -2.307052e+00 -1.215512e+00 -6.751710e-01
## lapse_zoffset[99] -2.035158e+00 -7.088305e-01 -4.458883e-02
## lapse_zoffset[100] -2.130454e+00 -9.308732e-01 -3.412101e-01
## lapse_zoffset[101] -1.496645e+00 -7.898089e-02 4.442207e-01
## lapse_zoffset[102] -2.314287e+00 -1.088338e+00 -5.512061e-01
## lapse_zoffset[103] 1.194445e+00 1.480649e+00 1.655531e+00
## lapse_zoffset[104] -2.182969e+00 -9.925095e-01 -4.084660e-01
## lapse_zoffset[105] -2.002799e+00 -8.438503e-01 -3.020723e-01
## lapse_zoffset[106] -1.605450e+00 -3.755799e-01 1.726428e-01
## lapse_zoffset[107] -2.027202e+00 -7.308654e-01 -1.263391e-01
## lapse_zoffset[108] -2.045719e+00 -9.888317e-01 -4.796535e-01
## lapse_zoffset[109] -2.191535e+00 -1.004788e+00 -4.325846e-01
## lapse_zoffset[110] 2.743600e-02 9.436741e-01 1.171849e+00
## lapse_zoffset[111] -2.277216e+00 -1.055113e+00 -4.589309e-01
## lapse_zoffset[112] -2.203162e+00 -1.038924e+00 -5.319016e-01
## lapse_zoffset[113] -2.227849e+00 -1.100427e+00 -5.813119e-01
## lapse_zoffset[114] -8.444234e-02 8.866046e-01 1.157789e+00
## lapse_zoffset[115] -2.194734e+00 -1.027932e+00 -5.035910e-01
## lapse_zoffset[116] -2.236952e+00 -9.687567e-01 -4.195371e-01
## lapse_zoffset[117] -1.449952e+00 -1.703625e-01 3.216850e-01
## lapse_zoffset[118] 8.189743e-01 1.261335e+00 1.443205e+00
## lapse_zoffset[119] -2.147275e+00 -1.022849e+00 -5.503169e-01
## lapse_zoffset[120] -2.016174e+00 -9.546331e-01 -3.679183e-01
## lapse_zoffset[121] -2.256230e+00 -1.061400e+00 -5.823967e-01
## lapse_zoffset[122] -2.196770e+00 -1.029894e+00 -4.971672e-01
## lapse_zoffset[123] -2.158437e+00 -1.020894e+00 -4.716398e-01
## lapse_zoffset[124] -2.144214e+00 -9.103895e-01 -3.410332e-01
## lapse_zoffset[125] -2.197900e+00 -1.029025e+00 -4.517640e-01
## lapse_zoffset[126] -1.425224e+00 1.547340e-01 6.209025e-01
## lapse_zoffset[127] -1.745267e+00 -3.865903e-01 2.442427e-01
## lapse_zoffset[128] 8.983390e-01 1.292524e+00 1.478936e+00
## lapse_zoffset[129] -2.186965e+00 -1.112194e+00 -5.624777e-01
## lapse_zoffset[130] -1.885397e+00 -5.910675e-01 1.644106e-02
## lapse_zoffset[131] -2.078088e+00 -9.798771e-01 -4.687371e-01
## lapse_zoffset[132] -8.580367e-01 4.794476e-01 7.810829e-01
## lapse_zoffset[133] -2.296737e+00 -1.093269e+00 -5.622871e-01
## lapse_zoffset[134] -2.088958e+00 -9.357073e-01 -3.222833e-01
## lapse_zoffset[135] 1.391122e+00 1.687986e+00 1.853502e+00
## lapse_zoffset[136] -2.032515e+00 -8.133093e-01 -2.305345e-01
## lapse_zoffset[137] -2.084497e+00 -9.793386e-01 -4.478057e-01
## lapse_zoffset[138] -2.093041e+00 -9.283479e-01 -4.069956e-01
## lapse_zoffset[139] -2.128480e+00 -8.576969e-01 -2.608065e-01
## lapse_zoffset[140] -2.287320e+00 -1.112382e+00 -5.236536e-01
## lapse_zoffset[141] -2.014061e+00 -7.444282e-01 -1.146002e-01
## lapse_zoffset[142] -1.060320e+00 3.250459e-01 6.828431e-01
## lapse_zoffset[143] -2.194498e+00 -1.059124e+00 -5.047569e-01
## lapse_zoffset[144] -1.904372e+00 -5.769570e-01 -2.823085e-02
## lapse_zoffset[145] -8.441908e-01 4.837999e-01 7.762898e-01
## lapse_zoffset[146] -1.331396e+00 1.388618e-01 5.745322e-01
## lapse_zoffset[147] -2.227095e+00 -1.219303e+00 -7.204623e-01
## lapse_zoffset[148] -1.004425e+00 3.369353e-01 6.882381e-01
## lapse_zoffset[149] -2.166143e+00 -1.029893e+00 -5.240935e-01
## lapse_zoffset[150] -2.204334e+00 -1.041394e+00 -4.940344e-01
## threshold[1] 2.015446e+00 2.417360e+00 2.579557e+00
## threshold[2] 1.902994e+00 2.262482e+00 2.414378e+00
## threshold[3] 1.817073e+00 2.197688e+00 2.364115e+00
## threshold[4] 1.845751e+00 2.205722e+00 2.371228e+00
## threshold[5] 1.792519e+00 2.173234e+00 2.354061e+00
## threshold[6] 1.769580e+00 2.136080e+00 2.292127e+00
## threshold[7] 1.916951e+00 2.275364e+00 2.439775e+00
## threshold[8] 1.747853e+00 2.143851e+00 2.319228e+00
## threshold[9] 1.908053e+00 2.275860e+00 2.443406e+00
## threshold[10] 1.812416e+00 2.214965e+00 2.385812e+00
## threshold[11] 1.877976e+00 2.231471e+00 2.389406e+00
## threshold[12] 1.863815e+00 2.205034e+00 2.359575e+00
## threshold[13] 1.988869e+00 2.375202e+00 2.548107e+00
## threshold[14] 1.741130e+00 2.153859e+00 2.331935e+00
## threshold[15] 1.963547e+00 2.305711e+00 2.461815e+00
## threshold[16] 1.753725e+00 2.116446e+00 2.283233e+00
## threshold[17] 1.818624e+00 2.184609e+00 2.340326e+00
## threshold[18] 1.839730e+00 2.240644e+00 2.420962e+00
## threshold[19] 1.942941e+00 2.384807e+00 2.556255e+00
## threshold[20] 2.022971e+00 2.401778e+00 2.555789e+00
## threshold[21] 1.902435e+00 2.211527e+00 2.385821e+00
## threshold[22] 1.787469e+00 2.135916e+00 2.298963e+00
## threshold[23] 1.938798e+00 2.307510e+00 2.456930e+00
## threshold[24] 1.964732e+00 2.379265e+00 2.554218e+00
## threshold[25] 2.129882e+00 2.482234e+00 2.665920e+00
## threshold[26] 1.858542e+00 2.214452e+00 2.395711e+00
## threshold[27] 2.058855e+00 2.428627e+00 2.601150e+00
## threshold[28] 2.062775e+00 2.451424e+00 2.626446e+00
## threshold[29] 2.187921e+00 2.517767e+00 2.716048e+00
## threshold[30] 1.906327e+00 2.229734e+00 2.412794e+00
## threshold[31] 1.809056e+00 2.173205e+00 2.338597e+00
## threshold[32] 2.010586e+00 2.405142e+00 2.601319e+00
## threshold[33] 1.791212e+00 2.289426e+00 2.472559e+00
## threshold[34] 1.974672e+00 2.380263e+00 2.534478e+00
## threshold[35] 2.036319e+00 2.428393e+00 2.590361e+00
## threshold[36] 1.727193e+00 2.113643e+00 2.295628e+00
## threshold[37] 1.842233e+00 2.233312e+00 2.402165e+00
## threshold[38] 1.896587e+00 2.267515e+00 2.427275e+00
## threshold[39] 1.682807e+00 2.068595e+00 2.249858e+00
## threshold[40] 1.836638e+00 2.243928e+00 2.423495e+00
## threshold[41] 2.016564e+00 2.394404e+00 2.566487e+00
## threshold[42] 1.833629e+00 2.198540e+00 2.384998e+00
## threshold[43] 1.912106e+00 2.272137e+00 2.436101e+00
## threshold[44] 1.770989e+00 2.163606e+00 2.321743e+00
## threshold[45] 1.774522e+00 2.153590e+00 2.318286e+00
## threshold[46] 1.955202e+00 2.366770e+00 2.549839e+00
## threshold[47] 1.636296e+00 2.030553e+00 2.206032e+00
## threshold[48] 1.839221e+00 2.234105e+00 2.409853e+00
## threshold[49] 1.828804e+00 2.226442e+00 2.410685e+00
## threshold[50] 1.796543e+00 2.202441e+00 2.379737e+00
## threshold[51] 1.789054e+00 2.184123e+00 2.349823e+00
## threshold[52] 1.897180e+00 2.274886e+00 2.448164e+00
## threshold[53] 1.709326e+00 2.057290e+00 2.236578e+00
## threshold[54] 1.909683e+00 2.239345e+00 2.425331e+00
## threshold[55] 2.128071e+00 2.470074e+00 2.637017e+00
## threshold[56] 1.907253e+00 2.290025e+00 2.466817e+00
## threshold[57] 1.677547e+00 2.068384e+00 2.234967e+00
## threshold[58] 1.911030e+00 2.238837e+00 2.412559e+00
## threshold[59] 1.965240e+00 2.281223e+00 2.484532e+00
## threshold[60] 1.908230e+00 2.261262e+00 2.443285e+00
## threshold[61] 1.910070e+00 2.258551e+00 2.443781e+00
## threshold[62] 1.786924e+00 2.163236e+00 2.334221e+00
## threshold[63] 1.859105e+00 2.220114e+00 2.400706e+00
## threshold[64] 1.907195e+00 2.264802e+00 2.436048e+00
## threshold[65] 1.907403e+00 2.324596e+00 2.497438e+00
## threshold[66] 1.969624e+00 2.286210e+00 2.479299e+00
## threshold[67] 1.882218e+00 2.264980e+00 2.438810e+00
## threshold[68] 2.091591e+00 2.439537e+00 2.631802e+00
## threshold[69] 1.771043e+00 2.118590e+00 2.283781e+00
## threshold[70] 1.831355e+00 2.226679e+00 2.409581e+00
## threshold[71] 2.012772e+00 2.402716e+00 2.561002e+00
## threshold[72] 1.905634e+00 2.261378e+00 2.431204e+00
## threshold[73] 1.840631e+00 2.206399e+00 2.375129e+00
## threshold[74] 1.991528e+00 2.362798e+00 2.529715e+00
## threshold[75] 2.082024e+00 2.437143e+00 2.600962e+00
## threshold[76] 1.825401e+00 2.208289e+00 2.368731e+00
## threshold[77] 1.645020e+00 2.000880e+00 2.172503e+00
## threshold[78] 1.884761e+00 2.244187e+00 2.414640e+00
## threshold[79] 1.820715e+00 2.232404e+00 2.421641e+00
## threshold[80] 1.882950e+00 2.240587e+00 2.414282e+00
## threshold[81] 1.713437e+00 2.095336e+00 2.275590e+00
## threshold[82] 2.107141e+00 2.447320e+00 2.620331e+00
## threshold[83] 2.118676e+00 2.454405e+00 2.613695e+00
## threshold[84] 2.014350e+00 2.351151e+00 2.521971e+00
## threshold[85] 1.771042e+00 2.115364e+00 2.283451e+00
## threshold[86] 1.833346e+00 2.184481e+00 2.356222e+00
## threshold[87] 1.882177e+00 2.247499e+00 2.411754e+00
## threshold[88] 2.107403e+00 2.441049e+00 2.609184e+00
## threshold[89] 2.070665e+00 2.436947e+00 2.616551e+00
## threshold[90] 1.985242e+00 2.330786e+00 2.498547e+00
## threshold[91] 1.688398e+00 2.096209e+00 2.267550e+00
## threshold[92] 1.897081e+00 2.237862e+00 2.429711e+00
## threshold[93] 1.852120e+00 2.225805e+00 2.388443e+00
## threshold[94] 1.799405e+00 2.183163e+00 2.365737e+00
## threshold[95] 1.881576e+00 2.231840e+00 2.404259e+00
## threshold[96] 1.771461e+00 2.160849e+00 2.355787e+00
## threshold[97] 1.943644e+00 2.348506e+00 2.519075e+00
## threshold[98] 1.696683e+00 2.038780e+00 2.214831e+00
## threshold[99] 2.094659e+00 2.452987e+00 2.623899e+00
## threshold[100] 1.877892e+00 2.254653e+00 2.414411e+00
## threshold[101] 1.807416e+00 2.193854e+00 2.368673e+00
## threshold[102] 1.935381e+00 2.332064e+00 2.503168e+00
## threshold[103] 1.997325e+00 2.385745e+00 2.561229e+00
## threshold[104] 1.761282e+00 2.125653e+00 2.287347e+00
## threshold[105] 2.008624e+00 2.380419e+00 2.534912e+00
## threshold[106] 1.877043e+00 2.228345e+00 2.401268e+00
## threshold[107] 2.275637e+00 2.595545e+00 2.881193e+00
## threshold[108] 1.790613e+00 2.132291e+00 2.314098e+00
## threshold[109] 1.828579e+00 2.206261e+00 2.366571e+00
## threshold[110] 1.832674e+00 2.231965e+00 2.404148e+00
## threshold[111] 1.892056e+00 2.241810e+00 2.407323e+00
## threshold[112] 1.874870e+00 2.188584e+00 2.376195e+00
## threshold[113] 1.752582e+00 2.106702e+00 2.263066e+00
## threshold[114] 1.804642e+00 2.202157e+00 2.368261e+00
## threshold[115] 1.810681e+00 2.159427e+00 2.317696e+00
## threshold[116] 1.896911e+00 2.235775e+00 2.384454e+00
## threshold[117] 2.089173e+00 2.448989e+00 2.625567e+00
## threshold[118] 1.852019e+00 2.242847e+00 2.398429e+00
## threshold[119] 1.932906e+00 2.254970e+00 2.439741e+00
## threshold[120] 1.879835e+00 2.222633e+00 2.376187e+00
## threshold[121] 1.868844e+00 2.201227e+00 2.373424e+00
## threshold[122] 1.894382e+00 2.214416e+00 2.359777e+00
## threshold[123] 1.847608e+00 2.212778e+00 2.381928e+00
## threshold[124] 1.939666e+00 2.301472e+00 2.465051e+00
## threshold[125] 2.132935e+00 2.459851e+00 2.649852e+00
## threshold[126] 1.911578e+00 2.267235e+00 2.425976e+00
## threshold[127] 1.994336e+00 2.305184e+00 2.472508e+00
## threshold[128] 1.778969e+00 2.192722e+00 2.366646e+00
## threshold[129] 1.709995e+00 2.099303e+00 2.263870e+00
## threshold[130] 2.071304e+00 2.461843e+00 2.631535e+00
## threshold[131] 2.004660e+00 2.388780e+00 2.544884e+00
## threshold[132] 1.872130e+00 2.216157e+00 2.406980e+00
## threshold[133] 1.763585e+00 2.148179e+00 2.323661e+00
## threshold[134] 1.962168e+00 2.292251e+00 2.449114e+00
## threshold[135] 1.778810e+00 2.158757e+00 2.350027e+00
## threshold[136] 1.916399e+00 2.280586e+00 2.456415e+00
## threshold[137] 1.991524e+00 2.358843e+00 2.518931e+00
## threshold[138] 2.087539e+00 2.450724e+00 2.620376e+00
## threshold[139] 1.997746e+00 2.318352e+00 2.494528e+00
## threshold[140] 1.798104e+00 2.184135e+00 2.355861e+00
## threshold[141] 1.833808e+00 2.189791e+00 2.364469e+00
## threshold[142] 2.055153e+00 2.421451e+00 2.603107e+00
## threshold[143] 1.945528e+00 2.262564e+00 2.425261e+00
## threshold[144] 1.859000e+00 2.223312e+00 2.403990e+00
## threshold[145] 1.824930e+00 2.180300e+00 2.355674e+00
## threshold[146] 1.928151e+00 2.282201e+00 2.449351e+00
## threshold[147] 1.568069e+00 1.945455e+00 2.121726e+00
## threshold[148] 2.036339e+00 2.415065e+00 2.575399e+00
## threshold[149] 1.877868e+00 2.283673e+00 2.449972e+00
## threshold[150] 1.807765e+00 2.181014e+00 2.346126e+00
## spread[1] 1.003485e+00 1.430647e+00 1.711189e+00
## spread[2] 1.116350e+00 1.572439e+00 1.816267e+00
## spread[3] 1.048643e+00 1.414476e+00 1.658331e+00
## spread[4] 1.434557e+00 1.883901e+00 2.148127e+00
## spread[5] 1.242134e+00 1.727180e+00 2.043305e+00
## spread[6] 8.652277e-01 1.146284e+00 1.321033e+00
## spread[7] 1.210243e+00 1.591506e+00 1.825932e+00
## spread[8] 1.152902e+00 1.683080e+00 2.050222e+00
## spread[9] 7.895780e-01 1.074793e+00 1.255010e+00
## spread[10] 1.154325e+00 1.581368e+00 1.907708e+00
## spread[11] 9.369900e-01 1.336824e+00 1.583822e+00
## spread[12] 1.050329e+00 1.423645e+00 1.635976e+00
## spread[13] 9.153622e-01 1.205320e+00 1.388918e+00
## spread[14] 1.019977e+00 1.486061e+00 1.784998e+00
## spread[15] 1.079046e+00 1.585305e+00 1.906015e+00
## spread[16] 9.708629e-01 1.286084e+00 1.494571e+00
## spread[17] 9.622068e-01 1.425644e+00 1.663123e+00
## spread[18] 8.772734e-01 1.170440e+00 1.364269e+00
## spread[19] 9.019420e-01 1.314392e+00 1.560442e+00
## spread[20] 1.048118e+00 1.374708e+00 1.568547e+00
## spread[21] 1.376554e+00 1.796741e+00 2.037639e+00
## spread[22] 1.154765e+00 1.485057e+00 1.702885e+00
## spread[23] 1.088988e+00 1.499190e+00 1.736689e+00
## spread[24] 8.890022e-01 1.311387e+00 1.562990e+00
## spread[25] 1.103469e+00 1.615817e+00 1.891920e+00
## spread[26] 1.139069e+00 1.622827e+00 1.955754e+00
## spread[27] 1.009708e+00 1.303603e+00 1.471194e+00
## spread[28] 1.157692e+00 1.562365e+00 1.821103e+00
## spread[29] 1.116656e+00 1.450610e+00 1.643058e+00
## spread[30] 1.204637e+00 1.634502e+00 1.960844e+00
## spread[31] 9.316573e-01 1.216924e+00 1.411975e+00
## spread[32] 9.872595e-01 1.387706e+00 1.680806e+00
## spread[33] 1.161198e+00 1.519732e+00 1.732536e+00
## spread[34] 1.061164e+00 1.392554e+00 1.595386e+00
## spread[35] 9.633021e-01 1.341850e+00 1.531286e+00
## spread[36] 1.028123e+00 1.361019e+00 1.567087e+00
## spread[37] 1.029345e+00 1.479372e+00 1.770301e+00
## spread[38] 1.152728e+00 1.489055e+00 1.690330e+00
## spread[39] 1.222396e+00 1.619666e+00 1.885682e+00
## spread[40] 8.394574e-01 1.125304e+00 1.289178e+00
## spread[41] 9.204242e-01 1.305731e+00 1.546305e+00
## spread[42] 1.148208e+00 1.602865e+00 1.901472e+00
## spread[43] 9.924926e-01 1.454506e+00 1.774806e+00
## spread[44] 1.067031e+00 1.365845e+00 1.556704e+00
## spread[45] 1.066359e+00 1.435918e+00 1.646779e+00
## spread[46] 8.927948e-01 1.290575e+00 1.537705e+00
## spread[47] 8.091919e-01 1.145164e+00 1.341406e+00
## spread[48] 9.185297e-01 1.247004e+00 1.433207e+00
## spread[49] 8.926880e-01 1.149716e+00 1.341130e+00
## spread[50] 1.159715e+00 1.705716e+00 2.020380e+00
## spread[51] 1.276781e+00 1.822996e+00 2.114936e+00
## spread[52] 1.272336e+00 1.673452e+00 1.935407e+00
## spread[53] 9.455593e-01 1.296213e+00 1.512545e+00
## spread[54] 1.126532e+00 1.512932e+00 1.736723e+00
## spread[55] 1.059840e+00 1.358235e+00 1.559240e+00
## spread[56] 7.883205e-01 1.087688e+00 1.261612e+00
## spread[57] 9.890681e-01 1.336337e+00 1.536204e+00
## spread[58] 9.883727e-01 1.326464e+00 1.537936e+00
## spread[59] 1.392006e+00 1.816421e+00 2.088148e+00
## spread[60] 1.241989e+00 1.694479e+00 2.022908e+00
## spread[61] 1.370772e+00 1.722022e+00 1.965423e+00
## spread[62] 9.333131e-01 1.380980e+00 1.643273e+00
## spread[63] 1.289760e+00 1.812570e+00 2.125116e+00
## spread[64] 1.360407e+00 1.858998e+00 2.157694e+00
## spread[65] 1.251519e+00 1.597954e+00 1.823534e+00
## spread[66] 1.265710e+00 1.737843e+00 1.991438e+00
## spread[67] 8.732074e-01 1.138896e+00 1.322986e+00
## spread[68] 9.455115e-01 1.323698e+00 1.586153e+00
## spread[69] 6.876186e-01 9.596102e-01 1.130433e+00
## spread[70] 9.622540e-01 1.352725e+00 1.565091e+00
## spread[71] 1.120043e+00 1.529104e+00 1.796829e+00
## spread[72] 1.039018e+00 1.492168e+00 1.751725e+00
## spread[73] 1.130091e+00 1.569295e+00 1.856497e+00
## spread[74] 1.033929e+00 1.361525e+00 1.563889e+00
## spread[75] 1.137460e+00 1.479484e+00 1.669176e+00
## spread[76] 9.359552e-01 1.358892e+00 1.629117e+00
## spread[77] 6.007705e-01 8.723761e-01 1.030716e+00
## spread[78] 9.697015e-01 1.279663e+00 1.473679e+00
## spread[79] 1.059036e+00 1.449675e+00 1.655217e+00
## spread[80] 1.128012e+00 1.639840e+00 1.956557e+00
## spread[81] 1.179459e+00 1.599098e+00 1.875160e+00
## spread[82] 1.167565e+00 1.529737e+00 1.754914e+00
## spread[83] 9.817304e-01 1.300845e+00 1.488143e+00
## spread[84] 7.563903e-01 1.055755e+00 1.222616e+00
## spread[85] 7.592024e-01 1.050700e+00 1.233348e+00
## spread[86] 9.943764e-01 1.389898e+00 1.639654e+00
## spread[87] 9.526242e-01 1.370287e+00 1.669171e+00
## spread[88] 1.130610e+00 1.494808e+00 1.701014e+00
## spread[89] 1.035643e+00 1.448144e+00 1.713400e+00
## spread[90] 1.292092e+00 1.774382e+00 2.057045e+00
## spread[91] 8.516132e-01 1.175448e+00 1.347549e+00
## spread[92] 1.312337e+00 1.728547e+00 1.979494e+00
## spread[93] 1.035938e+00 1.472235e+00 1.764997e+00
## spread[94] 1.048329e+00 1.539676e+00 1.821650e+00
## spread[95] 1.166100e+00 1.508352e+00 1.706295e+00
## spread[96] 9.305274e-01 1.327072e+00 1.609481e+00
## spread[97] 9.176228e-01 1.340227e+00 1.618779e+00
## spread[98] 8.692047e-01 1.206561e+00 1.419334e+00
## spread[99] 1.188853e+00 1.594628e+00 1.828319e+00
## spread[100] 1.210493e+00 1.536367e+00 1.749161e+00
## spread[101] 1.372351e+00 1.977950e+00 2.389472e+00
## spread[102] 9.625553e-01 1.248570e+00 1.430207e+00
## spread[103] 9.077250e-01 1.354159e+00 1.620935e+00
## spread[104] 1.071453e+00 1.508915e+00 1.739456e+00
## spread[105] 9.802263e-01 1.368803e+00 1.576651e+00
## spread[106] 1.298587e+00 1.783113e+00 2.082979e+00
## spread[107] 1.157421e+00 1.633776e+00 1.920082e+00
## spread[108] 1.215193e+00 1.614819e+00 1.848442e+00
## spread[109] 1.053881e+00 1.396151e+00 1.593852e+00
## spread[110] 1.182253e+00 1.675535e+00 2.024930e+00
## spread[111] 1.021412e+00 1.310893e+00 1.496419e+00
## spread[112] 1.111218e+00 1.491710e+00 1.713482e+00
## spread[113] 1.041632e+00 1.408329e+00 1.622999e+00
## spread[114] 1.010609e+00 1.420997e+00 1.726630e+00
## spread[115] 1.064700e+00 1.384523e+00 1.580581e+00
## spread[116] 9.840157e-01 1.307838e+00 1.501553e+00
## spread[117] 1.023894e+00 1.437193e+00 1.672852e+00
## spread[118] 9.831963e-01 1.408882e+00 1.683724e+00
## spread[119] 1.110513e+00 1.469350e+00 1.672928e+00
## spread[120] 1.290623e+00 1.674824e+00 1.892842e+00
## spread[121] 1.135842e+00 1.488165e+00 1.688433e+00
## spread[122] 8.554827e-01 1.144960e+00 1.313931e+00
## spread[123] 1.028194e+00 1.313953e+00 1.485439e+00
## spread[124] 1.205100e+00 1.529054e+00 1.736256e+00
## spread[125] 1.061377e+00 1.382307e+00 1.552106e+00
## spread[126] 1.020484e+00 1.441443e+00 1.720752e+00
## spread[127] 1.155283e+00 1.639439e+00 1.914948e+00
## spread[128] 8.571550e-01 1.260105e+00 1.507658e+00
## spread[129] 8.751100e-01 1.152387e+00 1.336897e+00
## spread[130] 1.205553e+00 1.580243e+00 1.823439e+00
## spread[131] 8.718726e-01 1.151424e+00 1.333295e+00
## spread[132] 1.129722e+00 1.635842e+00 1.978983e+00
## spread[133] 1.073731e+00 1.431289e+00 1.639261e+00
## spread[134] 1.202453e+00 1.524448e+00 1.735579e+00
## spread[135] 1.029498e+00 1.498139e+00 1.778897e+00
## spread[136] 1.345736e+00 1.724832e+00 1.988598e+00
## spread[137] 9.234276e-01 1.224225e+00 1.410463e+00
## spread[138] 9.908901e-01 1.318942e+00 1.496152e+00
## spread[139] 1.196866e+00 1.534439e+00 1.753737e+00
## spread[140] 9.105375e-01 1.193126e+00 1.373024e+00
## spread[141] 1.261274e+00 1.771368e+00 2.054886e+00
## spread[142] 7.917322e-01 1.193855e+00 1.480833e+00
## spread[143] 9.661966e-01 1.261772e+00 1.452317e+00
## spread[144] 1.201460e+00 1.645244e+00 1.902913e+00
## spread[145] 1.109700e+00 1.588134e+00 1.932464e+00
## spread[146] 9.890363e-01 1.401872e+00 1.652143e+00
## spread[147] 7.395999e-01 1.052439e+00 1.265607e+00
## spread[148] 9.926537e-01 1.394217e+00 1.656599e+00
## spread[149] 9.480756e-01 1.227347e+00 1.393923e+00
## spread[150] 9.621937e-01 1.253194e+00 1.433384e+00
## lapse[1] 1.862806e-02 7.685073e-02 1.031480e-01
## lapse[2] 1.338580e-04 2.514337e-03 9.700088e-03
## lapse[3] 3.160492e-04 5.220687e-03 1.341203e-02
## lapse[4] 1.971069e-04 2.391477e-03 7.607194e-03
## lapse[5] 4.909504e-04 8.292307e-03 2.284962e-02
## lapse[6] 9.654459e-05 1.113309e-03 3.136737e-03
## lapse[7] 1.121081e-04 1.972007e-03 7.742765e-03
## lapse[8] 6.171119e-04 2.058655e-02 4.335979e-02
## lapse[9] 1.045154e-04 1.150315e-03 3.248251e-03
## lapse[10] 3.991871e-04 1.971607e-02 4.461387e-02
## lapse[11] 2.723164e-04 6.752498e-03 1.841728e-02
## lapse[12] 1.440165e-04 1.715254e-03 4.761348e-03
## lapse[13] 1.159124e-04 1.242629e-03 3.440108e-03
## lapse[14] 9.505213e-02 1.475934e-01 1.744357e-01
## lapse[15] 2.416834e-04 6.096375e-03 2.235444e-02
## lapse[16] 9.827976e-05 1.287495e-03 3.604929e-03
## lapse[17] 1.085617e-04 2.007489e-03 6.482874e-03
## lapse[18] 1.347784e-04 1.159971e-03 3.512811e-03
## lapse[19] 2.241605e-01 2.771021e-01 3.046910e-01
## lapse[20] 1.089038e-04 1.225493e-03 4.050120e-03
## lapse[21] 1.650123e-04 2.262622e-03 7.183850e-03
## lapse[22] 1.362121e-04 1.436182e-03 4.157442e-03
## lapse[23] 9.825347e-05 2.050983e-03 6.913714e-03
## lapse[24] 2.898946e-01 3.474464e-01 3.798539e-01
## lapse[25] 3.899245e-04 8.897656e-03 2.826352e-02
## lapse[26] 6.079860e-04 1.563292e-02 3.844180e-02
## lapse[27] 8.670530e-05 1.318659e-03 3.748326e-03
## lapse[28] 2.063673e-04 2.968271e-03 1.030534e-02
## lapse[29] 1.771731e-04 1.541366e-03 4.844242e-03
## lapse[30] 5.371612e-03 6.549939e-02 9.257691e-02
## lapse[31] 8.436602e-05 1.160332e-03 3.388248e-03
## lapse[32] 1.691988e-02 7.663291e-02 1.033199e-01
## lapse[33] 1.010285e-04 1.603724e-03 4.788128e-03
## lapse[34] 1.432645e-04 1.831564e-03 5.968115e-03
## lapse[35] 1.643119e-04 1.728987e-03 5.521313e-03
## lapse[36] 8.863038e-05 1.115952e-03 3.543479e-03
## lapse[37] 3.396759e-02 9.436839e-02 1.227799e-01
## lapse[38] 8.932090e-05 1.369005e-03 4.584789e-03
## lapse[39] 1.625303e-04 1.947349e-03 5.808058e-03
## lapse[40] 1.159081e-04 1.103071e-03 3.047022e-03
## lapse[41] 2.382751e-04 4.000365e-03 1.252020e-02
## lapse[42] 1.163313e-01 1.749524e-01 2.068451e-01
## lapse[43] 5.428410e-04 1.675542e-02 3.903915e-02
## lapse[44] 8.857251e-05 1.271598e-03 3.802717e-03
## lapse[45] 1.651857e-04 1.611397e-03 4.959311e-03
## lapse[46] 2.738234e-01 3.307950e-01 3.601106e-01
## lapse[47] 1.324566e-04 1.312124e-03 3.432336e-03
## lapse[48] 1.001053e-04 1.198990e-03 3.613711e-03
## lapse[49] 8.404685e-05 1.130343e-03 3.206820e-03
## lapse[50] 1.094658e-01 1.732893e-01 2.030255e-01
## lapse[51] 1.564021e-04 2.991576e-03 1.003994e-02
## lapse[52] 1.284649e-04 1.984520e-03 8.308575e-03
## lapse[53] 1.585016e-04 1.646485e-03 4.849302e-03
## lapse[54] 1.633338e-04 1.930653e-03 5.642764e-03
## lapse[55] 8.409044e-05 1.345611e-03 4.194530e-03
## lapse[56] 1.149408e-04 1.141508e-03 3.087619e-03
## lapse[57] 8.931156e-05 1.305733e-03 3.656386e-03
## lapse[58] 1.294304e-04 1.493912e-03 4.564614e-03
## lapse[59] 1.673908e-04 2.392483e-03 8.084363e-03
## lapse[60] 5.855828e-04 1.161389e-02 2.817972e-02
## lapse[61] 1.632041e-04 2.130865e-03 6.502528e-03
## lapse[62] 4.050010e-04 5.392964e-03 1.411595e-02
## lapse[63] 2.893607e-04 3.986764e-03 1.269279e-02
## lapse[64] 3.265945e-04 6.572363e-03 1.966209e-02
## lapse[65] 1.093831e-04 1.312900e-03 4.481642e-03
## lapse[66] 1.858574e-04 3.448270e-03 1.119829e-02
## lapse[67] 8.014590e-05 9.991442e-04 2.925887e-03
## lapse[68] 1.471444e-03 2.826011e-02 4.875798e-02
## lapse[69] 8.617233e-05 9.625368e-04 2.686692e-03
## lapse[70] 1.281635e-04 1.553727e-03 5.170802e-03
## lapse[71] 2.496988e-04 4.805774e-03 1.593789e-02
## lapse[72] 1.175933e-01 1.683990e-01 1.970302e-01
## lapse[73] 3.160771e-04 5.336802e-03 1.508131e-02
## lapse[74] 1.401791e-04 1.453475e-03 3.896204e-03
## lapse[75] 1.318694e-04 1.469581e-03 4.373331e-03
## lapse[76] 2.826305e-04 6.787184e-03 1.846716e-02
## lapse[77] 8.077324e-05 8.564736e-04 2.401979e-03
## lapse[78] 8.958576e-05 1.169512e-03 3.345699e-03
## lapse[79] 1.330888e-04 1.568685e-03 5.298265e-03
## lapse[80] 6.524055e-04 1.046614e-02 2.716744e-02
## lapse[81] 3.007886e-04 4.499835e-03 1.223385e-02
## lapse[82] 1.194469e-04 2.332570e-03 7.325438e-03
## lapse[83] 1.114058e-04 1.243722e-03 3.764072e-03
## lapse[84] 1.077154e-04 1.113650e-03 3.432138e-03
## lapse[85] 8.214161e-05 9.825729e-04 2.786454e-03
## lapse[86] 1.181673e-02 5.786912e-02 8.091580e-02
## lapse[87] 2.848502e-03 4.798434e-02 7.231502e-02
## lapse[88] 1.614019e-04 1.861343e-03 6.265490e-03
## lapse[89] 7.658773e-04 1.316425e-02 3.091526e-02
## lapse[90] 1.599114e-04 3.189582e-03 1.387713e-02
## lapse[91] 6.982380e-05 9.681621e-04 2.980274e-03
## lapse[92] 1.804090e-04 2.358479e-03 8.078499e-03
## lapse[93] 5.949610e-04 2.256946e-02 4.435555e-02
## lapse[94] 1.176400e-01 1.735612e-01 2.019976e-01
## lapse[95] 1.077887e-04 1.257238e-03 3.905043e-03
## lapse[96] 7.851800e-03 6.259003e-02 8.484765e-02
## lapse[97] 2.127347e-01 2.716302e-01 3.017465e-01
## lapse[98] 1.187972e-04 1.189099e-03 3.628395e-03
## lapse[99] 1.260436e-04 2.400352e-03 8.921718e-03
## lapse[100] 1.092670e-04 1.360155e-03 4.600223e-03
## lapse[101] 4.341203e-04 1.057921e-02 3.228107e-02
## lapse[102] 9.936642e-05 1.128050e-03 3.579170e-03
## lapse[103] 1.308642e-01 1.777911e-01 2.040431e-01
## lapse[104] 1.274173e-04 1.796906e-03 5.926595e-03
## lapse[105] 1.586155e-04 1.801392e-03 5.900426e-03
## lapse[106] 3.157125e-04 6.310197e-03 2.009147e-02
## lapse[107] 1.511605e-04 2.229166e-03 8.092793e-03
## lapse[108] 1.739688e-04 1.894076e-03 5.323654e-03
## lapse[109] 6.540011e-05 1.194999e-03 3.597850e-03
## lapse[110] 1.383554e-02 8.846264e-02 1.190447e-01
## lapse[111] 7.592497e-05 1.092919e-03 3.507261e-03
## lapse[112] 1.175810e-04 1.767334e-03 4.964840e-03
## lapse[113] 1.512114e-04 1.442208e-03 4.482276e-03
## lapse[114] 5.805784e-03 5.287524e-02 7.830018e-02
## lapse[115] 9.178905e-05 1.114517e-03 3.269562e-03
## lapse[116] 7.964445e-05 1.248574e-03 3.869812e-03
## lapse[117] 5.578390e-04 7.378691e-03 1.906361e-02
## lapse[118] 5.462989e-02 1.028546e-01 1.296731e-01
## lapse[119] 1.377531e-04 1.622860e-03 4.878493e-03
## lapse[120] 1.290705e-04 1.286455e-03 4.227164e-03
## lapse[121] 1.353838e-04 1.527653e-03 4.437809e-03
## lapse[122] 7.955778e-05 1.088537e-03 3.183720e-03
## lapse[123] 1.067037e-04 1.122734e-03 3.383523e-03
## lapse[124] 1.058276e-04 1.397226e-03 4.431948e-03
## lapse[125] 1.112852e-04 1.226405e-03 4.371321e-03
## lapse[126] 3.753190e-04 1.225391e-02 2.975008e-02
## lapse[127] 2.035298e-04 3.801046e-03 1.426358e-02
## lapse[128] 6.868599e-02 1.100640e-01 1.346118e-01
## lapse[129] 9.157421e-05 9.970844e-04 2.918003e-03
## lapse[130] 1.657591e-04 3.167976e-03 1.049768e-02
## lapse[131] 1.382229e-04 1.367689e-03 4.163384e-03
## lapse[132] 1.837265e-03 3.633608e-02 6.173944e-02
## lapse[133] 1.125981e-04 1.635744e-03 4.507122e-03
## lapse[134] 1.039115e-04 1.297856e-03 4.690335e-03
## lapse[135] 2.473833e-01 3.026066e-01 3.328702e-01
## lapse[136] 1.294819e-04 1.618248e-03 5.400168e-03
## lapse[137] 1.294842e-04 1.477317e-03 4.250563e-03
## lapse[138] 1.286747e-04 1.552450e-03 4.646570e-03
## lapse[139] 1.072463e-04 1.518602e-03 5.035239e-03
## lapse[140] 8.804912e-05 9.623558e-04 2.993641e-03
## lapse[141] 1.979886e-04 2.775041e-03 1.053927e-02
## lapse[142] 1.290526e-03 1.897683e-02 3.850032e-02
## lapse[143] 7.908669e-05 1.050180e-03 3.169748e-03
## lapse[144] 2.502124e-04 4.303049e-03 1.270996e-02
## lapse[145] 2.093406e-03 3.609933e-02 5.999529e-02
## lapse[146] 4.294001e-04 1.196582e-02 2.624900e-02
## lapse[147] 1.212909e-04 1.261087e-03 3.217014e-03
## lapse[148] 1.282098e-03 2.063016e-02 3.880061e-02
## lapse[149] 1.282137e-04 1.222558e-03 3.531850e-03
## lapse[150] 7.828616e-05 1.083608e-03 3.197566e-03
## lp__ -6.523772e+03 -6.500023e+03 -6.486300e+03
## 75% 97.5% n_eff Rhat
## sigma_log_threshold 1.469579e-01 2.060819e-01 166.4705 1.0053572
## sigma_log_spread 2.982381e-01 3.785282e-01 188.1767 1.0152957
## sigma_logit_lapse 2.130261e+00 2.482343e+00 534.2332 1.0043465
## b_threshold[1] 9.758064e-01 1.030429e+00 1745.0463 0.9997879
## b_threshold[2] 9.020340e-01 9.687447e-01 2160.9429 0.9999632
## b_threshold[3] 9.004993e-01 9.681132e-01 1942.9611 0.9993030
## b_spread[1] 4.989232e-01 5.933792e-01 1323.7726 1.0029470
## b_spread[2] 5.358259e-01 6.355901e-01 506.9196 1.0047280
## b_spread[3] 6.615675e-01 7.845559e-01 626.7374 1.0055835
## b_lapse[1] -4.326248e+00 -3.822421e+00 608.0269 1.0006736
## b_lapse[2] -4.451679e+00 -3.891186e+00 405.8351 1.0018698
## b_lapse[3] -4.008164e+00 -3.517492e+00 483.2393 1.0086742
## threshold_zoffset[1] 7.858541e-01 2.074654e+00 3609.5962 0.9996557
## threshold_zoffset[2] 7.742180e-01 1.931233e+00 3319.8144 0.9991405
## threshold_zoffset[3] 4.979258e-01 1.695896e+00 3467.4552 0.9997988
## threshold_zoffset[4] 6.689382e-01 1.788479e+00 2900.6591 0.9992115
## threshold_zoffset[5] 6.788609e-01 1.849909e+00 3060.9606 0.9997678
## threshold_zoffset[6] 1.826523e-01 1.309883e+00 1922.1615 1.0013407
## threshold_zoffset[7] 8.839182e-01 2.106645e+00 3069.5424 0.9995265
## threshold_zoffset[8] 5.106507e-01 1.718732e+00 2721.8085 1.0005418
## threshold_zoffset[9] 8.781003e-02 1.321168e+00 1442.2717 0.9995855
## threshold_zoffset[10] 6.520794e-01 1.904849e+00 3144.6535 0.9991866
## threshold_zoffset[11] 6.118175e-01 1.850301e+00 2824.3703 0.9998624
## threshold_zoffset[12] 6.251963e-01 1.734154e+00 3260.9769 0.9991292
## threshold_zoffset[13] 5.676083e-01 1.708528e+00 3362.0205 0.9998581
## threshold_zoffset[14] 5.850041e-01 1.769982e+00 3235.0569 0.9997765
## threshold_zoffset[15] 1.067931e+00 2.237031e+00 3099.2095 0.9992985
## threshold_zoffset[16] 3.511976e-01 1.573815e+00 2782.6729 0.9995221
## threshold_zoffset[17] 3.852863e-01 1.499374e+00 2897.0324 0.9998643
## threshold_zoffset[18] 6.505960e-02 1.362431e+00 1703.8860 0.9994909
## threshold_zoffset[19] 6.658562e-01 2.027950e+00 3266.8859 0.9995443
## threshold_zoffset[20] 6.147608e-01 1.932124e+00 3613.1074 0.9991100
## threshold_zoffset[21] 7.624301e-01 1.971244e+00 2818.3652 0.9994477
## threshold_zoffset[22] 4.080978e-01 1.586506e+00 2864.1208 0.9990853
## threshold_zoffset[23] 9.409391e-01 2.183757e+00 1977.1129 1.0003816
## threshold_zoffset[24] 6.610699e-01 1.889601e+00 3413.1620 0.9998345
## threshold_zoffset[25] 1.157479e+00 2.424758e+00 2131.5339 1.0007100
## threshold_zoffset[26] 8.265319e-01 2.089616e+00 2728.9775 1.0002104
## threshold_zoffset[27] 7.599540e-01 1.884961e+00 3767.2413 0.9994231
## threshold_zoffset[28] 8.953148e-01 2.171252e+00 2433.0722 1.0014440
## threshold_zoffset[29] 1.266103e+00 2.387224e+00 1658.1068 0.9998111
## threshold_zoffset[30] 9.826926e-01 2.223573e+00 2781.7547 0.9992372
## threshold_zoffset[31] 4.290239e-01 1.592607e+00 2478.4117 0.9997631
## threshold_zoffset[32] 8.407523e-01 2.185344e+00 2652.3018 0.9997316
## threshold_zoffset[33] 2.580964e-01 1.513537e+00 2302.6811 0.9991046
## threshold_zoffset[34] 5.525402e-01 1.763524e+00 2819.5143 0.9990862
## threshold_zoffset[35] 7.347893e-01 1.929713e+00 2345.0178 1.0007581
## threshold_zoffset[36] 2.322596e-01 1.379853e+00 2256.6154 0.9992642
## threshold_zoffset[37] 7.579462e-01 2.141801e+00 2457.4304 0.9997252
## threshold_zoffset[38] 8.446260e-01 1.975197e+00 2962.0889 0.9993558
## threshold_zoffset[39] 1.958739e-01 1.444463e+00 2378.1773 0.9999577
## threshold_zoffset[40] 2.713628e-02 1.219611e+00 1839.2496 0.9993968
## threshold_zoffset[41] 6.305700e-01 1.839063e+00 2350.8899 0.9994067
## threshold_zoffset[42] 8.023876e-01 2.055290e+00 3208.0801 0.9991124
## threshold_zoffset[43] 8.752704e-01 1.960970e+00 2853.9799 1.0004535
## threshold_zoffset[44] 3.008784e-01 1.390744e+00 2896.5080 0.9998649
## threshold_zoffset[45] 5.318673e-01 1.850796e+00 3019.7239 1.0004762
## threshold_zoffset[46] 5.989937e-01 1.997259e+00 3410.1618 0.9997614
## threshold_zoffset[47] 5.632716e-02 1.279481e+00 1634.8974 0.9994490
## threshold_zoffset[48] 4.188516e-02 1.255703e+00 2184.8541 0.9992926
## threshold_zoffset[49] -6.321500e-03 1.138273e+00 1930.1944 0.9998255
## threshold_zoffset[50] 8.356462e-01 2.294378e+00 2802.0113 0.9990671
## threshold_zoffset[51] 6.611330e-01 1.900850e+00 2537.5654 0.9992715
## threshold_zoffset[52] 9.493552e-01 2.215294e+00 2985.0644 0.9994169
## threshold_zoffset[53] 1.737455e-01 1.365791e+00 1417.0228 1.0008349
## threshold_zoffset[54] 8.945019e-01 2.052905e+00 2952.4252 0.9994623
## threshold_zoffset[55] 9.334255e-01 2.072795e+00 1770.7843 1.0007603
## threshold_zoffset[56] 2.497349e-01 1.524681e+00 2105.9999 0.9993256
## threshold_zoffset[57] 1.474414e-01 1.274075e+00 2293.6307 0.9995354
## threshold_zoffset[58] 8.424080e-01 1.928461e+00 2583.6675 0.9996014
## threshold_zoffset[59] 1.214608e+00 2.436311e+00 1788.7264 0.9999406
## threshold_zoffset[60] 9.874460e-01 2.174301e+00 3205.6612 0.9997935
## threshold_zoffset[61] 1.068573e+00 2.308099e+00 2495.6447 0.9992080
## threshold_zoffset[62] 5.798317e-01 1.726259e+00 3011.4212 0.9996787
## threshold_zoffset[63] 8.585555e-01 2.080160e+00 3079.0233 1.0008273
## threshold_zoffset[64] 1.016425e+00 2.191258e+00 2310.9618 1.0002090
## threshold_zoffset[65] 3.567078e-01 1.510185e+00 2854.2846 1.0003828
## threshold_zoffset[66] 1.225343e+00 2.467917e+00 2109.1983 0.9997095
## threshold_zoffset[67] 1.383168e-01 1.422636e+00 1922.3728 0.9996802
## threshold_zoffset[68] 9.546742e-01 2.121475e+00 2391.6629 0.9991073
## threshold_zoffset[69] 1.927065e-01 1.347533e+00 2106.2988 1.0004749
## threshold_zoffset[70] 4.677645e-02 1.300499e+00 1887.5544 1.0004563
## threshold_zoffset[71] 6.879392e-01 1.807339e+00 3156.1960 1.0003869
## threshold_zoffset[72] 9.328221e-01 2.138740e+00 2384.0318 0.9997127
## threshold_zoffset[73] 7.366234e-01 1.958613e+00 2783.5872 0.9998281
## threshold_zoffset[74] 4.730170e-01 1.571482e+00 3624.2677 0.9993394
## threshold_zoffset[75] 8.126329e-01 1.990167e+00 2743.6761 0.9991223
## threshold_zoffset[76] 5.653806e-01 1.813849e+00 2792.9078 0.9992222
## threshold_zoffset[77] -3.121742e-01 9.031790e-01 1454.0674 0.9993194
## threshold_zoffset[78] 7.401000e-01 1.884773e+00 3187.8657 0.9992323
## threshold_zoffset[79] 1.013214e-01 1.239305e+00 1531.1571 1.0008150
## threshold_zoffset[80] 9.487678e-01 2.107488e+00 2788.0834 0.9999682
## threshold_zoffset[81] 3.417901e-01 1.485068e+00 2899.4715 1.0003772
## threshold_zoffset[82] 9.941310e-01 2.048171e+00 2501.6232 0.9995496
## threshold_zoffset[83] 8.280174e-01 2.043645e+00 2889.4474 0.9996008
## threshold_zoffset[84] 4.429583e-01 1.648008e+00 2450.3935 1.0006402
## threshold_zoffset[85] 1.447400e-01 1.291854e+00 1900.7533 0.9994639
## threshold_zoffset[86] 6.921997e-01 1.795847e+00 3243.3856 1.0005691
## threshold_zoffset[87] 8.381546e-01 2.042604e+00 3496.1128 0.9993998
## threshold_zoffset[88] 8.073126e-01 1.908636e+00 2974.8819 0.9998263
## threshold_zoffset[89] 9.144240e-01 2.095628e+00 2434.9096 0.9995619
## threshold_zoffset[90] 1.191398e+00 2.419951e+00 1648.6034 0.9998045
## threshold_zoffset[91] 9.509401e-02 1.254443e+00 1928.9170 0.9992299
## threshold_zoffset[92] 9.910589e-01 2.170041e+00 2871.9520 0.9990750
## threshold_zoffset[93] 6.956384e-01 1.898906e+00 2929.2352 0.9991694
## threshold_zoffset[94] 6.866961e-01 1.940090e+00 3412.6148 0.9994882
## threshold_zoffset[95] 6.932328e-01 1.918065e+00 2437.0496 1.0020599
## threshold_zoffset[96] 5.313559e-01 1.772253e+00 2504.9994 0.9999300
## threshold_zoffset[97] 5.125748e-01 1.810696e+00 2916.4558 0.9992021
## threshold_zoffset[98] 8.632054e-02 1.426833e+00 2070.2915 0.9991183
## threshold_zoffset[99] 8.835271e-01 2.035701e+00 3017.7058 0.9995208
## threshold_zoffset[100] 7.484293e-01 1.959980e+00 2708.2529 0.9998273
## threshold_zoffset[101] 7.360177e-01 1.986838e+00 3608.0298 0.9997411
## threshold_zoffset[102] 3.718339e-01 1.609327e+00 2472.4021 0.9992539
## threshold_zoffset[103] 7.302483e-01 1.943264e+00 3790.7601 0.9993023
## threshold_zoffset[104] 3.719914e-01 1.580763e+00 2013.0413 0.9996976
## threshold_zoffset[105] 5.092498e-01 1.730912e+00 2602.9341 0.9998100
## threshold_zoffset[106] 8.488072e-01 1.967294e+00 3254.2634 0.9994914
## threshold_zoffset[107] 2.031903e+00 3.494835e+00 614.1251 1.0009639
## threshold_zoffset[108] 5.421769e-01 1.723639e+00 3263.2322 0.9993440
## threshold_zoffset[109] 5.339654e-01 1.695183e+00 3387.3577 0.9990986
## threshold_zoffset[110] 8.553040e-01 2.135391e+00 2774.8595 1.0012833
## threshold_zoffset[111] 7.752137e-01 1.907900e+00 2387.9006 0.9993525
## threshold_zoffset[112] 7.339097e-01 1.903338e+00 3342.2415 0.9998131
## threshold_zoffset[113] 2.918663e-01 1.572098e+00 1928.8935 1.0008544
## threshold_zoffset[114] 5.527817e-01 1.818538e+00 2926.5215 0.9990374
## threshold_zoffset[115] 3.358443e-01 1.531514e+00 2920.6885 0.9992996
## threshold_zoffset[116] 6.194060e-01 1.761931e+00 3175.8235 0.9996047
## threshold_zoffset[117] 9.242925e-01 2.071268e+00 2467.9753 0.9991157
## threshold_zoffset[118] 7.032529e-01 2.012599e+00 2885.6507 0.9999957
## threshold_zoffset[119] 1.009879e+00 2.165961e+00 3041.8518 1.0001325
## threshold_zoffset[120] 5.702089e-01 1.804668e+00 2812.8309 0.9997857
## threshold_zoffset[121] 6.847273e-01 1.804729e+00 2540.0953 0.9994718
## threshold_zoffset[122] 5.308664e-01 1.718316e+00 3089.2488 0.9992266
## threshold_zoffset[123] 6.052157e-01 1.784208e+00 2909.2289 0.9993812
## threshold_zoffset[124] 1.011104e+00 2.095646e+00 2031.1374 0.9995932
## threshold_zoffset[125] 9.779850e-01 2.092523e+00 2077.9971 0.9990207
## threshold_zoffset[126] 9.136764e-01 2.159931e+00 3175.2200 0.9993203
## threshold_zoffset[127] 1.083626e+00 2.198528e+00 2160.2017 0.9994405
## threshold_zoffset[128] 5.611058e-01 1.800986e+00 3444.5220 0.9995426
## threshold_zoffset[129] 9.152149e-02 1.278252e+00 1851.6647 0.9998279
## threshold_zoffset[130] 9.177992e-01 2.097092e+00 2357.8840 0.9993777
## threshold_zoffset[131] 5.386109e-01 1.772672e+00 2430.2029 0.9992460
## threshold_zoffset[132] 8.805041e-01 2.155577e+00 3134.3584 0.9994180
## threshold_zoffset[133] 5.263233e-01 1.660168e+00 2950.9987 0.9990816
## threshold_zoffset[134] 9.659014e-01 2.220549e+00 2851.0725 1.0009141
## threshold_zoffset[135] 6.610659e-01 1.847567e+00 3604.3796 0.9992346
## threshold_zoffset[136] 9.670864e-01 2.213453e+00 2753.9190 0.9993653
## threshold_zoffset[137] 4.565306e-01 1.559765e+00 2746.5531 0.9999311
## threshold_zoffset[138] 8.581589e-01 1.977518e+00 2350.2275 0.9996607
## threshold_zoffset[139] 1.149502e+00 2.374797e+00 1743.9421 0.9999617
## threshold_zoffset[140] 5.210776e-01 1.758600e+00 2683.1810 0.9994212
## threshold_zoffset[141] 6.753827e-01 1.799934e+00 2668.4347 0.9994869
## threshold_zoffset[142] 8.747615e-01 1.980942e+00 2828.4029 0.9997059
## threshold_zoffset[143] 7.742023e-01 1.877388e+00 2415.3341 1.0001368
## threshold_zoffset[144] 7.957519e-01 1.992079e+00 2889.9381 0.9991754
## threshold_zoffset[145] 6.624290e-01 1.851852e+00 2586.6321 0.9993311
## threshold_zoffset[146] 9.189094e-01 2.154578e+00 2879.7293 1.0005553
## threshold_zoffset[147] -3.534751e-01 8.856257e-01 905.6538 1.0001379
## threshold_zoffset[148] 6.564037e-01 1.879797e+00 2860.4935 0.9997985
## threshold_zoffset[149] 2.065367e-01 1.355459e+00 2519.0055 0.9993398
## threshold_zoffset[150] 4.792134e-01 1.777841e+00 3262.6212 1.0003322
## spread_zoffset[1] 1.114136e+00 2.470703e+00 1658.6092 0.9994392
## spread_zoffset[2] 1.026611e+00 2.025149e+00 2165.9888 1.0004830
## spread_zoffset[3] 7.190184e-01 1.790635e+00 2952.1945 0.9992864
## spread_zoffset[4] 1.115291e+00 2.126896e+00 2307.5597 1.0009022
## spread_zoffset[5] 1.023468e+00 2.089152e+00 2188.9356 0.9999635
## spread_zoffset[6] -2.241830e-01 9.853665e-01 2563.6326 1.0005738
## spread_zoffset[7] 1.032512e+00 1.994768e+00 2259.2649 1.0007608
## spread_zoffset[8] 1.187942e+00 2.371340e+00 1421.4443 1.0033486
## spread_zoffset[9] -2.915033e-01 7.735787e-01 2874.2868 1.0023630
## spread_zoffset[10] 1.436665e+00 2.531136e+00 1222.4579 1.0014558
## spread_zoffset[11] 5.758569e-01 1.650836e+00 2495.3515 0.9993814
## spread_zoffset[12] 7.800700e-02 1.027627e+00 2672.1045 0.9992846
## spread_zoffset[13] 6.343726e-02 1.116861e+00 3073.6249 1.0000863
## spread_zoffset[14] 6.347723e-01 1.977697e+00 2933.4231 0.9995305
## spread_zoffset[15] 1.242665e+00 2.329062e+00 1884.9869 1.0018507
## spread_zoffset[16] -2.161378e-01 8.204771e-01 2857.8513 1.0000343
## spread_zoffset[17] 6.778347e-01 1.616943e+00 3014.0077 0.9993973
## spread_zoffset[18] 5.287162e-02 1.022211e+00 2317.8507 1.0001383
## spread_zoffset[19] 6.898855e-01 2.015756e+00 2670.2916 0.9993549
## spread_zoffset[20] 5.091983e-01 1.524902e+00 2773.8336 1.0000479
## spread_zoffset[21] 9.345827e-01 1.919444e+00 2292.4364 0.9995541
## spread_zoffset[22] 2.402498e-01 1.178710e+00 2455.7393 1.0000716
## spread_zoffset[23] 8.237384e-01 1.766791e+00 2407.1487 0.9991471
## spread_zoffset[24] 7.246442e-01 1.980662e+00 3323.4073 0.9997488
## spread_zoffset[25] 1.348081e+00 2.348533e+00 2301.3319 1.0007078
## spread_zoffset[26] 9.632822e-01 2.177498e+00 2011.7692 0.9993946
## spread_zoffset[27] 2.906631e-01 1.221850e+00 2583.1955 1.0009871
## spread_zoffset[28] 1.109172e+00 2.093541e+00 2556.0670 1.0001282
## spread_zoffset[29] 7.059487e-01 1.720952e+00 2023.3508 1.0009498
## spread_zoffset[30] 1.021643e+00 2.397751e+00 935.7410 1.0032493
## spread_zoffset[31] 3.564018e-02 1.105912e+00 2508.9393 0.9992169
## spread_zoffset[32] 1.040601e+00 2.542697e+00 1477.4744 1.0030785
## spread_zoffset[33] 8.913627e-01 1.850999e+00 2885.6971 0.9996004
## spread_zoffset[34] 6.060018e-01 1.698593e+00 2858.6485 0.9994846
## spread_zoffset[35] 4.248652e-01 1.595955e+00 3485.9958 0.9992002
## spread_zoffset[36] 4.241636e-01 1.448335e+00 2533.1014 0.9994193
## spread_zoffset[37] 1.116910e+00 2.506001e+00 2316.9223 0.9996973
## spread_zoffset[38] 7.013539e-01 1.774022e+00 2986.9126 0.9992665
## spread_zoffset[39] 6.954588e-01 1.730235e+00 2678.3174 0.9995715
## spread_zoffset[40] -2.002543e-01 8.974843e-01 2513.7882 1.0003000
## spread_zoffset[41] 5.752379e-01 1.668837e+00 2098.8410 1.0006321
## spread_zoffset[42] 9.122910e-01 2.191964e+00 1928.3584 0.9991111
## spread_zoffset[43] 1.138675e+00 2.291364e+00 1878.1851 0.9990337
## spread_zoffset[44] 3.745928e-01 1.428232e+00 3520.4613 1.0002863
## spread_zoffset[45] 1.460780e-01 1.127900e+00 2499.6022 1.0006455
## spread_zoffset[46] 6.686993e-01 1.970815e+00 2623.8621 0.9998536
## spread_zoffset[47] -6.454667e-01 5.103917e-01 2557.5918 1.0005931
## spread_zoffset[48] 2.019298e-01 1.363741e+00 2668.3997 1.0000987
## spread_zoffset[49] -7.060799e-02 9.728548e-01 2857.2202 0.9993322
## spread_zoffset[50] 1.073109e+00 2.388811e+00 3144.7262 0.9999044
## spread_zoffset[51] 1.112006e+00 2.090096e+00 1813.7490 1.0025506
## spread_zoffset[52] 1.211318e+00 2.215102e+00 2558.4310 0.9996607
## spread_zoffset[53] -1.432052e-01 9.515523e-01 2710.7752 0.9994025
## spread_zoffset[54] 3.249655e-01 1.312628e+00 2712.6841 1.0000357
## spread_zoffset[55] 5.203669e-01 1.422777e+00 2648.7406 0.9991303
## spread_zoffset[56] -2.815611e-01 8.674216e-01 2748.5718 0.9998290
## spread_zoffset[57] -1.365181e-01 9.192480e-01 3590.7643 0.9992716
## spread_zoffset[58] -1.079079e-01 8.784919e-01 2437.4342 0.9990972
## spread_zoffset[59] 1.014755e+00 1.930286e+00 2442.8354 0.9998867
## spread_zoffset[60] 1.020496e+00 2.130654e+00 2250.1607 0.9992642
## spread_zoffset[61] 7.480996e-01 1.779498e+00 2202.9978 1.0004953
## spread_zoffset[62] 2.423026e-01 1.351732e+00 2806.0035 0.9996130
## spread_zoffset[63] 1.071896e+00 2.175267e+00 2154.2326 0.9991941
## spread_zoffset[64] 1.176078e+00 2.246143e+00 1929.8006 1.0001791
## spread_zoffset[65] 1.071032e+00 2.006777e+00 3339.0688 0.9991163
## spread_zoffset[66] 8.620126e-01 1.822451e+00 2099.5908 0.9993227
## spread_zoffset[67] -9.058036e-02 9.598221e-01 3130.3630 0.9999847
## spread_zoffset[68] 7.792353e-01 2.056222e+00 1698.7587 0.9990765
## spread_zoffset[69] -8.414153e-01 2.633972e-01 2345.6247 1.0006934
## spread_zoffset[70] 5.604803e-01 1.633344e+00 2583.2494 1.0006679
## spread_zoffset[71] 1.127153e+00 2.128016e+00 2053.5794 1.0001383
## spread_zoffset[72] 1.018549e+00 2.262532e+00 2754.8120 1.0001736
## spread_zoffset[73] 6.701682e-01 1.701861e+00 2691.3719 1.0012602
## spread_zoffset[74] 5.159575e-01 1.653515e+00 2352.7436 0.9991466
## spread_zoffset[75] 7.642571e-01 1.692142e+00 3617.9773 0.9998072
## spread_zoffset[76] 7.028671e-01 1.750380e+00 2007.4109 0.9998906
## spread_zoffset[77] -1.156668e+00 8.883901e-02 1402.9022 0.9996497
## spread_zoffset[78] 1.603733e-01 1.122199e+00 2984.5839 0.9993655
## spread_zoffset[79] 7.890104e-01 1.782527e+00 3080.1049 1.0000266
## spread_zoffset[80] 8.710632e-01 2.004664e+00 1986.9088 0.9998718
## spread_zoffset[81] 7.163346e-01 1.786643e+00 2740.5189 0.9993748
## spread_zoffset[82] 1.022213e+00 2.006301e+00 1989.4206 0.9999831
## spread_zoffset[83] 3.665807e-01 1.408536e+00 2668.2957 1.0005994
## spread_zoffset[84] -3.755554e-01 7.400263e-01 2765.6068 1.0010597
## spread_zoffset[85] -4.830105e-01 7.413392e-01 2707.0427 0.9996513
## spread_zoffset[86] 3.333089e-01 1.773037e+00 1198.3819 0.9994163
## spread_zoffset[87] 1.013408e+00 2.403024e+00 1529.0642 1.0007487
## spread_zoffset[88] 8.705365e-01 1.756781e+00 2296.3461 0.9990583
## spread_zoffset[89] 1.011997e+00 2.168518e+00 1821.8179 0.9991993
## spread_zoffset[90] 1.504031e+00 2.444528e+00 2107.6137 1.0013144
## spread_zoffset[91] -1.415224e-01 9.593565e-01 3518.3124 0.9994122
## spread_zoffset[92] 8.349391e-01 1.773016e+00 2280.3782 0.9995795
## spread_zoffset[93] 1.109759e+00 2.304410e+00 1175.2522 0.9993429
## spread_zoffset[94] 7.386968e-01 2.182122e+00 2236.4540 0.9992450
## spread_zoffset[95] 7.392469e-01 1.722650e+00 2479.9454 1.0011148
## spread_zoffset[96] 8.189840e-01 2.312723e+00 929.2061 1.0031711
## spread_zoffset[97] 8.584651e-01 2.192129e+00 3292.4833 0.9992616
## spread_zoffset[98] -4.255525e-01 7.141994e-01 1888.8343 0.9996569
## spread_zoffset[99] 1.142748e+00 2.107249e+00 2161.3565 1.0000444
## spread_zoffset[100] 8.311094e-01 1.784956e+00 2529.1230 0.9990974
## spread_zoffset[101] 1.626999e+00 2.690446e+00 1658.3217 1.0005463
## spread_zoffset[102] 2.045089e-01 1.283325e+00 3041.3424 0.9999522
## spread_zoffset[103] 8.458207e-01 2.113733e+00 2890.4905 1.0020159
## spread_zoffset[104] 3.283740e-01 1.408447e+00 2775.2855 0.9998029
## spread_zoffset[105] 5.798870e-01 1.518721e+00 2153.0881 0.9997339
## spread_zoffset[106] 1.111268e+00 2.159019e+00 2342.7853 1.0006525
## spread_zoffset[107] 1.371625e+00 2.290355e+00 915.2226 1.0020697
## spread_zoffset[108] 5.390567e-01 1.603707e+00 2068.3543 0.9996243
## spread_zoffset[109] 4.590977e-01 1.509339e+00 3232.9981 0.9992978
## spread_zoffset[110] 1.137006e+00 2.600129e+00 1144.5069 1.0006029
## spread_zoffset[111] 2.478669e-01 1.285535e+00 2148.6901 1.0009146
## spread_zoffset[112] 2.576310e-01 1.329652e+00 2524.7499 1.0001099
## spread_zoffset[113] 8.668616e-02 1.122917e+00 2449.6347 0.9995095
## spread_zoffset[114] 9.980776e-01 2.433127e+00 1253.2130 0.9996806
## spread_zoffset[115] 4.691001e-01 1.466976e+00 2775.7087 0.9999784
## spread_zoffset[116] 2.795596e-01 1.344578e+00 2888.5219 0.9993775
## spread_zoffset[117] 8.697395e-01 1.908526e+00 2004.8969 1.0022765
## spread_zoffset[118] 9.141609e-01 2.272699e+00 2023.5587 1.0016608
## spread_zoffset[119] 1.550248e-01 1.128324e+00 2671.1056 1.0000440
## spread_zoffset[120] 1.105373e+00 2.106262e+00 2595.3390 1.0006448
## spread_zoffset[121] 1.771298e-01 1.237057e+00 2277.0739 1.0022826
## spread_zoffset[122] -2.961315e-01 7.185324e-01 3622.9595 1.0010511
## spread_zoffset[123] 2.411478e-01 1.247183e+00 3285.0275 0.9997545
## spread_zoffset[124] 7.969502e-01 1.788659e+00 2716.9999 0.9996458
## spread_zoffset[125] 4.982325e-01 1.450850e+00 2598.8383 1.0000500
## spread_zoffset[126] 9.594637e-01 2.169645e+00 1562.2305 1.0031568
## spread_zoffset[127] 1.165990e+00 2.154768e+00 2279.7765 0.9997958
## spread_zoffset[128] 4.336237e-01 1.849053e+00 1936.7195 1.0010635
## spread_zoffset[129] -1.526304e-01 9.044958e-01 3578.5235 0.9997757
## spread_zoffset[130] 1.109133e+00 2.014717e+00 2200.6213 1.0017181
## spread_zoffset[131] -8.926846e-02 1.013611e+00 3004.9301 0.9998534
## spread_zoffset[132] 1.039342e+00 2.367621e+00 1504.4160 1.0027227
## spread_zoffset[133] 1.217367e-01 1.217718e+00 2889.4412 0.9991322
## spread_zoffset[134] 7.879783e-01 1.736017e+00 2480.2878 0.9995939
## spread_zoffset[135] 5.973203e-01 1.876191e+00 2706.8766 1.0013398
## spread_zoffset[136] 1.316114e+00 2.261755e+00 2260.7847 0.9991965
## spread_zoffset[137] 1.249167e-01 1.193600e+00 3328.7853 1.0004375
## spread_zoffset[138] 3.519852e-01 1.345732e+00 2445.3518 0.9991008
## spread_zoffset[139] 8.177858e-01 1.769807e+00 1961.2961 0.9993942
## spread_zoffset[140] -3.293726e-02 9.423916e-01 3299.5709 0.9995984
## spread_zoffset[141] 1.004828e+00 2.072470e+00 2026.4586 1.0006808
## spread_zoffset[142] 5.697750e-01 1.808748e+00 1712.5052 1.0001219
## spread_zoffset[143] 1.664911e-01 1.221764e+00 3135.3471 0.9992520
## spread_zoffset[144] 6.923115e-01 1.658538e+00 2877.7835 1.0001119
## spread_zoffset[145] 1.047159e+00 2.202816e+00 1613.0784 1.0022256
## spread_zoffset[146] 8.004416e-01 2.031926e+00 1734.6049 0.9995829
## spread_zoffset[147] -8.151182e-01 3.476192e-01 3094.4203 1.0002972
## spread_zoffset[148] 9.627325e-01 2.142944e+00 1755.4826 1.0002961
## spread_zoffset[149] 6.312041e-02 1.036097e+00 2317.7654 1.0003871
## spread_zoffset[150] 7.612884e-02 1.076198e+00 2144.8329 0.9996068
## lapse_zoffset[1] 1.421472e+00 1.775474e+00 684.2549 1.0005507
## lapse_zoffset[2] 5.317742e-01 1.159945e+00 1568.1569 1.0024368
## lapse_zoffset[3] 5.981355e-01 1.157852e+00 1208.8798 1.0005537
## lapse_zoffset[4] 1.480562e-01 8.462105e-01 2234.6016 0.9991737
## lapse_zoffset[5] 6.247460e-01 1.086450e+00 969.0641 1.0029882
## lapse_zoffset[6] -1.705963e-02 6.980221e-01 2248.8229 0.9994333
## lapse_zoffset[7] 4.290510e-01 1.072211e+00 1553.5028 0.9992732
## lapse_zoffset[8] 8.562402e-01 1.261728e+00 576.3512 1.0045919
## lapse_zoffset[9] -1.008097e-01 5.937019e-01 2499.3781 0.9992963
## lapse_zoffset[10] 1.104287e+00 1.523275e+00 495.2027 1.0002021
## lapse_zoffset[11] 7.076932e-01 1.222407e+00 1246.0168 1.0005045
## lapse_zoffset[12] -8.338514e-02 5.761569e-01 1921.3206 0.9995549
## lapse_zoffset[13] -1.081394e-01 6.011061e-01 2110.5864 1.0011566
## lapse_zoffset[14] 1.567387e+00 1.880376e+00 677.0232 1.0036453
## lapse_zoffset[15] 8.789867e-01 1.426560e+00 768.9989 1.0034976
## lapse_zoffset[16] -1.945724e-01 5.243316e-01 2460.3161 0.9998540
## lapse_zoffset[17] 3.081010e-01 9.497304e-01 1882.3635 1.0009230
## lapse_zoffset[18] -8.096710e-02 6.424212e-01 1957.7664 0.9997073
## lapse_zoffset[19] 2.118206e+00 2.470206e+00 411.2709 1.0076437
## lapse_zoffset[20] 4.585539e-02 7.506412e-01 2579.6998 1.0010309
## lapse_zoffset[21] 1.596057e-01 8.376260e-01 1894.4471 0.9991852
## lapse_zoffset[22] -1.637946e-01 5.124828e-01 2191.5439 1.0004285
## lapse_zoffset[23] 4.072536e-01 1.081879e+00 1600.8439 0.9997031
## lapse_zoffset[24] 2.284180e+00 2.652908e+00 412.0609 1.0079929
## lapse_zoffset[25] 8.655882e-01 1.354994e+00 983.0603 1.0013934
## lapse_zoffset[26] 8.329428e-01 1.271672e+00 635.1815 1.0006291
## lapse_zoffset[27] -4.154842e-02 6.376057e-01 1950.6944 0.9990922
## lapse_zoffset[28] 4.713209e-01 1.071050e+00 1699.5130 1.0005544
## lapse_zoffset[29] 1.241700e-01 8.960301e-01 2417.6926 0.9995847
## lapse_zoffset[30] 1.213174e+00 1.556315e+00 409.8776 1.0010184
## lapse_zoffset[31] -2.737444e-03 7.187485e-01 1727.8418 0.9995764
## lapse_zoffset[32] 1.432525e+00 1.774135e+00 568.6396 1.0040258
## lapse_zoffset[33] 1.062547e-01 8.496684e-01 2320.1865 1.0005523
## lapse_zoffset[34] 1.931256e-01 8.417661e-01 2261.8747 0.9999117
## lapse_zoffset[35] 1.807392e-01 8.292970e-01 2111.0643 1.0006661
## lapse_zoffset[36] 3.298360e-02 8.088811e-01 2424.6490 0.9993417
## lapse_zoffset[37] 1.604583e+00 1.950244e+00 695.2469 1.0027423
## lapse_zoffset[38] 1.920326e-01 9.327281e-01 2192.9083 0.9996211
## lapse_zoffset[39] -1.014469e-02 6.199391e-01 1770.1429 0.9994507
## lapse_zoffset[40] -1.658288e-01 5.550920e-01 2053.2750 1.0001285
## lapse_zoffset[41] 5.042671e-01 1.056670e+00 1324.9954 1.0003176
## lapse_zoffset[42] 1.682359e+00 2.012007e+00 613.6296 1.0042936
## lapse_zoffset[43] 1.063634e+00 1.518257e+00 781.4806 1.0000835
## lapse_zoffset[44] 4.394260e-02 8.477977e-01 2641.7659 0.9996260
## lapse_zoffset[45] -7.347404e-02 6.093258e-01 2144.7822 0.9996038
## lapse_zoffset[46] 2.257185e+00 2.599852e+00 402.3685 1.0070761
## lapse_zoffset[47] -2.678056e-01 4.395032e-01 1972.5930 0.9993184
## lapse_zoffset[48] -5.897517e-02 6.665436e-01 2167.0039 0.9999136
## lapse_zoffset[49] -1.088589e-01 6.076646e-01 2050.4796 0.9994243
## lapse_zoffset[50] 1.672614e+00 2.004229e+00 660.3831 1.0067786
## lapse_zoffset[51] 3.523191e-01 9.361491e-01 1701.4667 1.0019132
## lapse_zoffset[52] 4.732450e-01 1.113740e+00 1677.0846 1.0023577
## lapse_zoffset[53] -6.166601e-02 5.822504e-01 2292.7636 0.9996681
## lapse_zoffset[54] 5.964714e-02 7.181439e-01 2164.8289 1.0004348
## lapse_zoffset[55] 4.216777e-02 7.702490e-01 2082.4630 1.0005592
## lapse_zoffset[56] -1.571474e-01 5.379213e-01 2183.9691 0.9994895
## lapse_zoffset[57] -1.993806e-01 5.162739e-01 2020.1075 0.9994241
## lapse_zoffset[58] -7.123120e-02 6.099523e-01 2097.0398 0.9991852
## lapse_zoffset[59] 2.193574e-01 8.861268e-01 1863.6289 1.0000572
## lapse_zoffset[60] 7.010614e-01 1.183536e+00 1177.8179 1.0014027
## lapse_zoffset[61] 6.283547e-02 7.993360e-01 1985.5918 0.9991831
## lapse_zoffset[62] 3.932908e-01 9.157418e-01 1442.5643 1.0006745
## lapse_zoffset[63] 4.312698e-01 9.718841e-01 1658.3570 0.9993801
## lapse_zoffset[64] 5.825570e-01 1.120801e+00 962.6186 1.0059567
## lapse_zoffset[65] 4.329887e-02 7.966173e-01 2190.6497 1.0006540
## lapse_zoffset[66] 3.953804e-01 9.336904e-01 1672.8117 0.9997241
## lapse_zoffset[67] -1.370704e-01 6.110865e-01 2929.7340 0.9994451
## lapse_zoffset[68] 1.038880e+00 1.430820e+00 676.7804 1.0005618
## lapse_zoffset[69] -1.418178e-01 5.395402e-01 2477.6054 0.9995280
## lapse_zoffset[70] 1.104060e-01 8.186416e-01 1913.6689 1.0000182
## lapse_zoffset[71] 6.543399e-01 1.174292e+00 1152.3497 1.0001473
## lapse_zoffset[72] 1.892142e+00 2.246093e+00 678.3628 1.0016416
## lapse_zoffset[73] 4.327342e-01 9.766765e-01 1454.5010 1.0010594
## lapse_zoffset[74] -5.374530e-03 7.398748e-01 2213.6880 0.9994574
## lapse_zoffset[75] 8.919433e-02 7.829922e-01 2505.4777 0.9993197
## lapse_zoffset[76] 7.242675e-01 1.253020e+00 1084.8198 0.9993344
## lapse_zoffset[77] -1.930499e-01 4.884018e-01 3135.5367 0.9991663
## lapse_zoffset[78] -1.021661e-02 7.204415e-01 2522.7420 0.9991216
## lapse_zoffset[79] 1.420595e-01 7.846235e-01 2109.8679 1.0008221
## lapse_zoffset[80] 6.658546e-01 1.125978e+00 1115.1113 0.9995261
## lapse_zoffset[81] 3.364649e-01 9.078212e-01 1612.9761 0.9997796
## lapse_zoffset[82] 3.884419e-01 1.005629e+00 1911.2279 1.0002907
## lapse_zoffset[83] -3.781703e-02 6.920551e-01 2015.8242 1.0003550
## lapse_zoffset[84] -9.394898e-02 6.407343e-01 2664.8681 0.9992940
## lapse_zoffset[85] -1.281612e-01 5.775111e-01 2415.0341 0.9993971
## lapse_zoffset[86] 1.145972e+00 1.503182e+00 395.9502 1.0017208
## lapse_zoffset[87] 1.327145e+00 1.700953e+00 364.3455 1.0108517
## lapse_zoffset[88] 2.741435e-01 9.165697e-01 2049.7408 0.9990204
## lapse_zoffset[89] 8.741184e-01 1.335721e+00 1081.7201 0.9993161
## lapse_zoffset[90] 7.232504e-01 1.268870e+00 1316.1718 0.9993091
## lapse_zoffset[91] -3.887691e-02 6.851499e-01 2044.3607 1.0040711
## lapse_zoffset[92] 2.257444e-01 8.292359e-01 2115.0356 0.9998513
## lapse_zoffset[93] 1.094493e+00 1.516049e+00 487.3410 1.0018768
## lapse_zoffset[94] 1.660315e+00 1.996536e+00 646.6387 1.0034283
## lapse_zoffset[95] 1.154981e-01 8.799225e-01 2280.7105 0.9991034
## lapse_zoffset[96] 1.399877e+00 1.732360e+00 443.8367 1.0064341
## lapse_zoffset[97] 2.104798e+00 2.449609e+00 425.6016 1.0097300
## lapse_zoffset[98] -2.163505e-01 5.039066e-01 2072.6235 0.9995327
## lapse_zoffset[99] 4.637315e-01 1.076194e+00 1718.1066 0.9992042
## lapse_zoffset[100] 1.809206e-01 8.994912e-01 2029.3925 0.9996805
## lapse_zoffset[101] 7.846698e-01 1.245469e+00 960.8016 1.0036116
## lapse_zoffset[102] -5.315129e-02 6.770861e-01 2284.4557 1.0019993
## lapse_zoffset[103] 1.833805e+00 2.166603e+00 457.3731 1.0085365
## lapse_zoffset[104] 5.304690e-02 7.091019e-01 1844.0056 0.9993826
## lapse_zoffset[105] 1.963606e-01 8.488365e-01 1703.9163 0.9996420
## lapse_zoffset[106] 5.916354e-01 1.110830e+00 1162.4620 1.0007583
## lapse_zoffset[107] 4.671779e-01 1.151785e+00 1398.3116 1.0032555
## lapse_zoffset[108] 4.768589e-03 6.205177e-01 1980.3368 0.9994721
## lapse_zoffset[109] 3.694343e-02 8.010064e-01 2613.3837 0.9996423
## lapse_zoffset[110] 1.348427e+00 1.695995e+00 394.5374 1.0014284
## lapse_zoffset[111] 4.230686e-02 7.770836e-01 2663.0395 0.9994589
## lapse_zoffset[112] -4.302386e-02 6.544701e-01 1981.6846 0.9999348
## lapse_zoffset[113] -1.387495e-01 5.728558e-01 2016.4836 0.9998466
## lapse_zoffset[114] 1.367141e+00 1.728895e+00 504.5092 0.9999203
## lapse_zoffset[115] 4.613522e-03 7.263643e-01 2551.8097 1.0002824
## lapse_zoffset[116] 6.244611e-02 8.169071e-01 2024.9061 0.9993681
## lapse_zoffset[117] 7.018194e-01 1.205322e+00 1227.5593 1.0039926
## lapse_zoffset[118] 1.631285e+00 1.963823e+00 711.9800 1.0008306
## lapse_zoffset[119] -7.303115e-02 6.344547e-01 2044.2267 1.0000987
## lapse_zoffset[120] 1.126993e-01 8.048572e-01 2267.8149 0.9999476
## lapse_zoffset[121] -1.402376e-01 5.748585e-01 2077.2903 1.0010775
## lapse_zoffset[122] -3.553801e-02 6.694404e-01 1647.5190 0.9994672
## lapse_zoffset[123] 3.687427e-02 7.750894e-01 1875.5130 0.9990694
## lapse_zoffset[124] 1.513032e-01 8.882159e-01 2267.3822 0.9993620
## lapse_zoffset[125] 6.668821e-02 7.728772e-01 2114.0561 0.9996190
## lapse_zoffset[126] 9.387690e-01 1.424941e+00 747.3518 1.0028875
## lapse_zoffset[127] 7.014011e-01 1.261169e+00 1618.2648 1.0008482
## lapse_zoffset[128] 1.672018e+00 1.986435e+00 612.9470 1.0055424
## lapse_zoffset[129] -1.076674e-01 6.270909e-01 1853.4806 1.0005517
## lapse_zoffset[130] 4.973842e-01 1.117400e+00 1687.4492 1.0012788
## lapse_zoffset[131] 3.689071e-03 6.839579e-01 2344.1254 0.9993752
## lapse_zoffset[132] 1.003534e+00 1.410348e+00 759.2455 1.0033386
## lapse_zoffset[133] -8.833832e-02 6.027015e-01 2382.6201 0.9998085
## lapse_zoffset[134] 1.910425e-01 9.267664e-01 1884.7303 1.0003555
## lapse_zoffset[135] 2.015036e+00 2.336336e+00 523.4099 1.0036528
## lapse_zoffset[136] 2.917924e-01 1.039884e+00 2053.8662 0.9991969
## lapse_zoffset[137] 2.476773e-02 7.459669e-01 2369.0932 0.9992186
## lapse_zoffset[138] 8.075929e-02 7.776351e-01 2343.8926 0.9996641
## lapse_zoffset[139] 2.607536e-01 9.674912e-01 1884.2114 0.9990120
## lapse_zoffset[140] -3.972119e-02 7.142285e-01 2226.9844 0.9999703
## lapse_zoffset[141] 3.499252e-01 9.564331e-01 1723.2024 1.0004403
## lapse_zoffset[142] 9.560164e-01 1.360241e+00 871.6547 1.0003210
## lapse_zoffset[143] -6.313177e-03 7.530539e-01 2037.6087 1.0000558
## lapse_zoffset[144] 4.064882e-01 9.908585e-01 1614.6439 1.0003700
## lapse_zoffset[145] 9.966665e-01 1.362926e+00 645.2005 1.0074037
## lapse_zoffset[146] 8.769335e-01 1.328813e+00 903.6062 1.0045786
## lapse_zoffset[147] -2.820644e-01 4.165466e-01 2314.3757 0.9993470
## lapse_zoffset[148] 9.743668e-01 1.441204e+00 805.1782 1.0012537
## lapse_zoffset[149] -4.774593e-02 6.348197e-01 2448.6478 0.9991497
## lapse_zoffset[150] -1.566121e-02 7.169786e-01 2406.1911 0.9995141
## threshold[1] 2.775604e+00 3.482801e+00 2561.9089 1.0002414
## threshold[2] 2.598185e+00 3.152893e+00 2667.3120 0.9994045
## threshold[3] 2.515013e+00 2.939852e+00 4338.4264 0.9994375
## threshold[4] 2.547429e+00 3.036408e+00 2738.9769 0.9997944
## threshold[5] 2.538238e+00 3.083864e+00 3127.5822 1.0000699
## threshold[6] 2.430017e+00 2.716663e+00 1865.7225 1.0007425
## threshold[7] 2.647744e+00 3.202064e+00 2462.8976 0.9995982
## threshold[8] 2.488647e+00 2.977588e+00 3211.1082 1.0008251
## threshold[9] 2.594966e+00 2.904110e+00 1488.7373 0.9998514
## threshold[10] 2.557153e+00 3.062996e+00 2919.8769 0.9997186
## threshold[11] 2.547033e+00 2.959555e+00 2970.0378 0.9996848
## threshold[12] 2.531754e+00 2.970965e+00 3072.9768 0.9991383
## threshold[13] 2.711637e+00 3.166716e+00 3383.7406 0.9994205
## threshold[14] 2.513366e+00 3.041521e+00 2936.3507 0.9993424
## threshold[15] 2.675533e+00 3.277551e+00 1938.5239 0.9991812
## threshold[16] 2.447167e+00 2.835451e+00 3179.5314 0.9994679
## threshold[17] 2.483340e+00 2.852992e+00 2845.8201 0.9993783
## threshold[18] 2.579869e+00 2.925124e+00 1519.2709 0.9999730
## threshold[19] 2.760906e+00 3.352842e+00 2866.5726 0.9994844
## threshold[20] 2.715200e+00 3.184777e+00 3184.6410 0.9994357
## threshold[21] 2.593059e+00 3.121864e+00 2135.9822 0.9995707
## threshold[22] 2.472141e+00 2.833652e+00 3305.3234 0.9993470
## threshold[23] 2.655703e+00 3.231340e+00 1455.0914 1.0016632
## threshold[24] 2.745348e+00 3.361116e+00 2642.4535 1.0001582
## threshold[25] 2.928737e+00 3.717690e+00 933.8654 1.0024732
## threshold[26] 2.610066e+00 3.181789e+00 2047.8134 0.9998710
## threshold[27] 2.782596e+00 3.301837e+00 2749.6963 0.9997059
## threshold[28] 2.843334e+00 3.480280e+00 1828.0196 1.0028878
## threshold[29] 2.999877e+00 3.645340e+00 816.3379 1.0015789
## threshold[30] 2.651721e+00 3.256472e+00 1385.0379 0.9997034
## threshold[31] 2.480746e+00 2.859445e+00 3196.2492 0.9991776
## threshold[32] 2.820334e+00 3.475840e+00 2029.9721 1.0000357
## threshold[33] 2.631466e+00 3.052051e+00 2041.8353 0.9996378
## threshold[34] 2.710292e+00 3.185474e+00 3051.1084 0.9992123
## threshold[35] 2.783506e+00 3.286670e+00 2400.3390 0.9994909
## threshold[36] 2.439018e+00 2.791420e+00 1905.5323 0.9992519
## threshold[37] 2.593168e+00 3.197920e+00 2327.8502 0.9996683
## threshold[38] 2.615714e+00 3.133953e+00 2080.9234 1.0001018
## threshold[39] 2.412252e+00 2.773985e+00 2532.9545 1.0002251
## threshold[40] 2.578535e+00 2.894796e+00 1233.1005 0.9998587
## threshold[41] 2.732535e+00 3.221272e+00 2503.8952 0.9992511
## threshold[42] 2.602541e+00 3.188796e+00 2197.5589 0.9995041
## threshold[43] 2.616753e+00 3.112319e+00 2332.8982 1.0007472
## threshold[44] 2.462845e+00 2.838808e+00 2955.1407 0.9998453
## threshold[45] 2.498984e+00 2.969883e+00 3181.8635 1.0009733
## threshold[46] 2.739336e+00 3.293792e+00 2641.8513 0.9998900
## threshold[47] 2.370601e+00 2.669077e+00 2076.3557 1.0004179
## threshold[48] 2.578055e+00 2.890409e+00 1483.7229 0.9994026
## threshold[49] 2.569936e+00 2.857137e+00 1454.9210 0.9999871
## threshold[50] 2.603768e+00 3.327474e+00 1823.7340 0.9996539
## threshold[51] 2.554090e+00 3.032986e+00 2435.8532 0.9997244
## threshold[52] 2.652919e+00 3.275852e+00 2031.6185 1.0013736
## threshold[53] 2.412106e+00 2.716711e+00 2056.6271 0.9995772
## threshold[54] 2.610898e+00 3.113192e+00 1938.0179 0.9990337
## threshold[55] 2.855823e+00 3.386493e+00 1522.5658 1.0011022
## threshold[56] 2.627350e+00 2.975719e+00 1688.2600 1.0010321
## threshold[57] 2.398421e+00 2.740834e+00 2657.0257 0.9999820
## threshold[58] 2.601195e+00 3.091265e+00 2077.6919 0.9997897
## threshold[59] 2.758678e+00 3.458734e+00 816.1415 1.0011721
## threshold[60] 2.672202e+00 3.236752e+00 1151.3115 1.0002990
## threshold[61] 2.689014e+00 3.313972e+00 1641.1103 0.9991768
## threshold[62] 2.523253e+00 2.952345e+00 3305.8114 0.9991100
## threshold[63] 2.608058e+00 3.226076e+00 2043.0677 1.0008503
## threshold[64] 2.652971e+00 3.311422e+00 1071.4996 1.0017964
## threshold[65] 2.660087e+00 3.070807e+00 3283.8387 0.9996953
## threshold[66] 2.732072e+00 3.443637e+00 977.6251 1.0015271
## threshold[67] 2.602273e+00 2.948785e+00 1774.6708 1.0003312
## threshold[68] 2.857367e+00 3.437591e+00 1793.2326 0.9996297
## threshold[69] 2.434725e+00 2.711346e+00 1450.6955 1.0000639
## threshold[70] 2.578507e+00 2.876477e+00 1292.4829 1.0011961
## threshold[71] 2.749613e+00 3.229646e+00 2559.0066 0.9998524
## threshold[72] 2.640758e+00 3.361013e+00 1419.5847 1.0035608
## threshold[73] 2.566797e+00 3.076180e+00 2445.7495 0.9995428
## threshold[74] 2.698730e+00 3.121903e+00 3235.3186 0.9991824
## threshold[75] 2.794581e+00 3.249068e+00 1803.1783 0.9994938
## threshold[76] 2.535448e+00 2.975370e+00 2632.7533 0.9992046
## threshold[77] 2.327094e+00 2.577128e+00 737.8989 0.9993467
## threshold[78] 2.593982e+00 3.050890e+00 3613.8695 0.9991727
## threshold[79] 2.586339e+00 2.899827e+00 1386.1271 1.0006764
## threshold[80] 2.635968e+00 3.173279e+00 2154.3165 0.9993434
## threshold[81] 2.448206e+00 2.859631e+00 3474.7970 0.9996764
## threshold[82] 2.856106e+00 3.512856e+00 1864.3512 0.9997547
## threshold[83] 2.803099e+00 3.292572e+00 2327.1576 0.9991521
## threshold[84] 2.685307e+00 3.055580e+00 2799.2853 1.0000367
## threshold[85] 2.428672e+00 2.699560e+00 1786.7208 0.9995947
## threshold[86] 2.555597e+00 3.022332e+00 2546.3566 1.0001269
## threshold[87] 2.609882e+00 3.170792e+00 2645.1507 0.9992260
## threshold[88] 2.794697e+00 3.295786e+00 2023.5441 1.0009371
## threshold[89] 2.843954e+00 3.444926e+00 1798.3828 1.0011983
## threshold[90] 2.754061e+00 3.484025e+00 1115.4526 1.0015418
## threshold[91] 2.420740e+00 2.684420e+00 1468.4039 0.9995586
## threshold[92] 2.634962e+00 3.250753e+00 1688.7211 0.9993978
## threshold[93] 2.562639e+00 3.069711e+00 3551.6783 0.9991734
## threshold[94] 2.563079e+00 3.127319e+00 2192.8929 0.9994862
## threshold[95] 2.567562e+00 3.098917e+00 2395.8014 1.0020421
## threshold[96] 2.520190e+00 2.982017e+00 2796.1748 1.0005915
## threshold[97] 2.708468e+00 3.208148e+00 2712.3081 0.9993139
## threshold[98] 2.388093e+00 2.685688e+00 2394.5794 0.9996073
## threshold[99] 2.833534e+00 3.467120e+00 2005.3272 0.9999977
## threshold[100] 2.588363e+00 3.077319e+00 2793.6561 1.0000652
## threshold[101] 2.563039e+00 3.149761e+00 2442.4313 1.0003192
## threshold[102] 2.660780e+00 3.067178e+00 2904.8319 0.9994000
## threshold[103] 2.755254e+00 3.378610e+00 2528.5855 0.9993447
## threshold[104] 2.456864e+00 2.858363e+00 2113.0659 0.9997850
## threshold[105] 2.701324e+00 3.157639e+00 3041.8524 0.9998483
## threshold[106] 2.604345e+00 3.168567e+00 2297.6040 0.9994176
## threshold[107] 3.371212e+00 4.547835e+00 357.8662 1.0055432
## threshold[108] 2.497231e+00 2.917602e+00 3212.4128 0.9998340
## threshold[109] 2.527986e+00 2.964049e+00 3321.2473 0.9993015
## threshold[110] 2.600087e+00 3.258328e+00 1646.8583 1.0030415
## threshold[111] 2.589401e+00 3.057919e+00 2753.4111 1.0004457
## threshold[112] 2.571028e+00 3.059327e+00 2054.6682 0.9991933
## threshold[113] 2.442019e+00 2.851866e+00 2961.7448 0.9995253
## threshold[114] 2.529864e+00 3.014890e+00 3147.1983 0.9991864
## threshold[115] 2.476407e+00 2.777468e+00 2770.5647 0.9992391
## threshold[116] 2.562102e+00 3.002557e+00 3425.3484 1.0003594
## threshold[117] 2.839088e+00 3.417349e+00 1818.9773 1.0004253
## threshold[118] 2.573940e+00 3.171108e+00 2765.1458 0.9995900
## threshold[119] 2.671436e+00 3.223625e+00 1426.9726 1.0003983
## threshold[120] 2.534144e+00 2.966314e+00 3251.7820 0.9994242
## threshold[121] 2.552421e+00 3.006369e+00 2344.9531 0.9992082
## threshold[122] 2.516899e+00 2.881171e+00 4061.5588 0.9992964
## threshold[123] 2.539130e+00 2.975546e+00 3525.5707 0.9990295
## threshold[124] 2.671502e+00 3.208700e+00 1438.1692 1.0009428
## threshold[125] 2.882744e+00 3.422145e+00 1720.1487 1.0001270
## threshold[126] 2.632380e+00 3.196899e+00 2535.5578 1.0004049
## threshold[127] 2.695362e+00 3.318542e+00 984.0626 1.0014504
## threshold[128] 2.530104e+00 3.015592e+00 2862.8715 1.0008397
## threshold[129] 2.407181e+00 2.710129e+00 1445.3164 1.0002681
## threshold[130] 2.853264e+00 3.466880e+00 1502.0021 1.0004765
## threshold[131] 2.709242e+00 3.130839e+00 2728.2793 0.9993353
## threshold[132] 2.621586e+00 3.220069e+00 1985.3092 0.9996837
## threshold[133] 2.506763e+00 2.928502e+00 3294.4780 0.9991778
## threshold[134] 2.651686e+00 3.208128e+00 1602.7203 1.0034303
## threshold[135] 2.549509e+00 3.110420e+00 3126.3575 0.9990353
## threshold[136] 2.676494e+00 3.331231e+00 1689.8452 1.0007113
## threshold[137] 2.682318e+00 3.064030e+00 2962.8306 0.9995535
## threshold[138] 2.818860e+00 3.325315e+00 2126.1656 0.9997264
## threshold[139] 2.737672e+00 3.387981e+00 1290.6651 1.0024262
## threshold[140] 2.504232e+00 2.915532e+00 3305.9059 0.9996130
## threshold[141] 2.556883e+00 3.014547e+00 2355.1970 0.9990943
## threshold[142] 2.823697e+00 3.404557e+00 2404.7735 1.0001627
## threshold[143] 2.596296e+00 3.026222e+00 3023.2360 0.9997978
## threshold[144] 2.598632e+00 3.102375e+00 2232.6155 0.9991226
## threshold[145] 2.535970e+00 3.049344e+00 2277.3689 0.9999304
## threshold[146] 2.641247e+00 3.169286e+00 2180.7794 1.0004548
## threshold[147] 2.291806e+00 2.583944e+00 735.6180 1.0003816
## threshold[148] 2.757933e+00 3.320042e+00 2895.9448 1.0009061
## threshold[149] 2.615801e+00 2.975590e+00 2143.6118 0.9991712
## threshold[150] 2.510461e+00 2.910528e+00 3238.2199 0.9994523
## spread[1] 2.091256e+00 3.292970e+00 1032.8268 1.0021629
## spread[2] 2.108063e+00 2.797122e+00 1250.4003 1.0055875
## spread[3] 1.938444e+00 2.668543e+00 1411.7630 1.0027850
## spread[4] 2.448625e+00 3.140414e+00 1373.5191 0.9998426
## spread[5] 2.437217e+00 3.333859e+00 1343.3470 1.0021674
## spread[6] 1.519953e+00 2.037450e+00 2186.3206 1.0005035
## spread[7] 2.114382e+00 2.795679e+00 1654.6318 1.0016032
## spread[8] 2.536425e+00 3.661368e+00 591.3533 1.0093142
## spread[9] 1.445857e+00 1.873883e+00 1233.3808 1.0029599
## spread[10] 2.367100e+00 3.473141e+00 555.5563 1.0011096
## spread[11] 1.885015e+00 2.585687e+00 1835.4171 0.9995158
## spread[12] 1.873518e+00 2.445918e+00 2456.0501 1.0001250
## spread[13] 1.589940e+00 2.096649e+00 2964.0646 0.9993938
## spread[14] 2.154211e+00 3.252486e+00 1851.5256 1.0005582
## spread[15] 2.269159e+00 3.052610e+00 805.1930 1.0063682
## spread[16] 1.709676e+00 2.268945e+00 2501.4676 0.9998379
## spread[17] 1.911864e+00 2.516584e+00 2372.3588 0.9995961
## spread[18] 1.563009e+00 2.029378e+00 2535.0124 0.9991874
## spread[19] 1.861189e+00 2.825815e+00 1994.5433 1.0001495
## spread[20] 1.778087e+00 2.312988e+00 2898.5226 1.0003119
## spread[21] 2.307407e+00 2.974228e+00 1794.8950 1.0019420
## spread[22] 1.935484e+00 2.469795e+00 3193.9511 0.9991110
## spread[23] 1.982426e+00 2.599777e+00 1709.0577 1.0017934
## spread[24] 1.886264e+00 2.815313e+00 2635.3659 1.0009610
## spread[25] 2.226557e+00 3.081131e+00 971.2226 1.0047735
## spread[26] 2.397916e+00 3.310233e+00 1197.0495 1.0011288
## spread[27] 1.676947e+00 2.190479e+00 2409.2438 0.9992238
## spread[28] 2.098397e+00 2.731909e+00 1763.6457 0.9996415
## spread[29] 1.894920e+00 2.432758e+00 1745.3150 1.0028746
## spread[30] 2.379670e+00 3.816483e+00 412.2333 1.0099141
## spread[31] 1.628584e+00 2.103440e+00 2559.6486 0.9992077
## spread[32] 2.033042e+00 3.453575e+00 699.1315 1.0076425
## spread[33] 1.960266e+00 2.534175e+00 2350.9115 1.0026945
## spread[34] 1.826526e+00 2.370852e+00 2674.9784 0.9994933
## spread[35] 1.746240e+00 2.304454e+00 3077.1450 0.9992160
## spread[36] 1.790187e+00 2.324130e+00 2787.8339 1.0000959
## spread[37] 2.173028e+00 3.424451e+00 864.2456 1.0032139
## spread[38] 1.930890e+00 2.617925e+00 2055.5797 1.0013086
## spread[39] 2.167666e+00 2.939013e+00 2282.8659 1.0009759
## spread[40] 1.482450e+00 1.946989e+00 1556.4634 1.0006555
## spread[41] 1.811609e+00 2.453597e+00 2197.7237 0.9998679
## spread[42] 2.303876e+00 3.554724e+00 1228.6814 1.0000335
## spread[43] 2.165724e+00 3.171483e+00 809.9125 1.0013721
## spread[44] 1.775732e+00 2.307044e+00 3191.0949 0.9994419
## spread[45] 1.903312e+00 2.447729e+00 2857.7821 0.9996139
## spread[46] 1.856956e+00 2.745228e+00 2397.9393 0.9996383
## spread[47] 1.559157e+00 2.136664e+00 1563.3461 1.0013958
## spread[48] 1.639189e+00 2.230489e+00 2730.0635 1.0001423
## spread[49] 1.543792e+00 1.958143e+00 2850.3329 0.9990216
## spread[50] 2.450206e+00 3.722047e+00 1277.8338 1.0012592
## spread[51] 2.445551e+00 3.189681e+00 1084.1074 1.0064335
## spread[52] 2.222769e+00 2.944704e+00 1400.1693 1.0002922
## spread[53] 1.768573e+00 2.286124e+00 2493.5997 0.9996838
## spread[54] 1.983307e+00 2.622958e+00 2254.9063 0.9993128
## spread[55] 1.792516e+00 2.298579e+00 2378.6170 0.9993784
## spread[56] 1.465752e+00 1.963576e+00 2080.4305 1.0013638
## spread[57] 1.774796e+00 2.329371e+00 2671.1082 0.9995165
## spread[58] 1.774322e+00 2.254568e+00 2252.9410 0.9998005
## spread[59] 2.391155e+00 3.123754e+00 1251.4875 1.0001287
## spread[60] 2.428111e+00 3.331489e+00 1443.3377 1.0006090
## spread[61] 2.232093e+00 2.898696e+00 2157.1124 1.0004330
## spread[62] 1.945844e+00 2.610597e+00 2188.2841 1.0004536
## spread[63] 2.425834e+00 3.261418e+00 1299.2627 1.0005164
## spread[64] 2.506179e+00 3.439060e+00 780.5810 1.0061172
## spread[65] 2.059772e+00 2.642683e+00 2231.6816 1.0011342
## spread[66] 2.288706e+00 3.024362e+00 1820.7142 1.0005370
## spread[67] 1.518524e+00 1.989446e+00 2084.5932 1.0006779
## spread[68] 1.916847e+00 2.861837e+00 1134.1167 0.9996626
## spread[69] 1.311154e+00 1.716120e+00 1252.8621 1.0021308
## spread[70] 1.814103e+00 2.371970e+00 2629.6447 0.9994589
## spread[71] 2.108856e+00 2.801444e+00 1791.0256 1.0009942
## spread[72] 2.108450e+00 3.155000e+00 1218.1045 1.0038933
## spread[73] 2.199867e+00 2.913223e+00 1642.0453 1.0028505
## spread[74] 1.785744e+00 2.371002e+00 2498.7579 0.9993171
## spread[75] 1.899353e+00 2.469460e+00 2373.9745 1.0006456
## spread[76] 1.940064e+00 2.635991e+00 1395.2634 1.0011971
## spread[77] 1.224756e+00 1.668102e+00 720.3936 1.0018025
## spread[78] 1.671988e+00 2.181012e+00 2851.7711 0.9996378
## spread[79] 1.914707e+00 2.472912e+00 2474.8816 0.9992153
## spread[80] 2.324015e+00 3.205422e+00 1545.8691 0.9997883
## spread[81] 2.202256e+00 3.007402e+00 2002.5500 0.9995153
## spread[82] 2.035280e+00 2.718364e+00 2130.8291 1.0001797
## spread[83] 1.709632e+00 2.234843e+00 2639.3953 1.0000397
## spread[84] 1.422825e+00 1.896951e+00 1798.0537 1.0012787
## spread[85] 1.427428e+00 1.902374e+00 1725.0933 0.9992004
## spread[86] 2.000934e+00 3.110510e+00 676.9056 0.9992055
## spread[87] 2.099452e+00 3.396870e+00 460.6772 1.0058745
## spread[88] 1.940896e+00 2.515044e+00 2352.8905 1.0000590
## spread[89] 2.061099e+00 2.899608e+00 1432.4715 1.0010980
## spread[90] 2.407045e+00 3.235547e+00 780.2179 1.0035827
## spread[91] 1.555395e+00 2.097821e+00 3193.8119 0.9992161
## spread[92] 2.243984e+00 2.969862e+00 2194.6376 1.0010696
## spread[93] 2.176111e+00 3.206344e+00 468.7492 1.0022979
## spread[94] 2.193789e+00 3.479370e+00 1352.2492 1.0001146
## spread[95] 1.958899e+00 2.518934e+00 2274.6648 0.9998410
## spread[96] 1.973706e+00 3.425992e+00 551.5403 1.0054626
## spread[97] 1.967841e+00 2.884412e+00 2245.0584 1.0003797
## spread[98] 1.654385e+00 2.175192e+00 1666.5537 0.9999262
## spread[99] 2.125307e+00 2.747544e+00 1519.4772 1.0030588
## spread[100] 1.986394e+00 2.569672e+00 2020.3014 1.0008943
## spread[101] 2.827704e+00 3.968658e+00 727.6259 1.0058231
## spread[102] 1.644970e+00 2.202056e+00 2737.4524 0.9994356
## spread[103] 1.946529e+00 2.902187e+00 1945.1400 1.0044765
## spread[104] 1.989926e+00 2.610496e+00 2501.9328 0.9995088
## spread[105] 1.797616e+00 2.361668e+00 2616.3223 0.9998272
## spread[106] 2.433102e+00 3.361475e+00 1127.6969 1.0012301
## spread[107] 2.258941e+00 3.027063e+00 621.2811 1.0031291
## spread[108] 2.103102e+00 2.741052e+00 2863.6420 0.9994492
## spread[109] 1.823360e+00 2.342359e+00 2792.2554 0.9996604
## spread[110] 2.482009e+00 4.104011e+00 530.8039 1.0026774
## spread[111] 1.719125e+00 2.224597e+00 2355.5237 1.0004666
## spread[112] 1.969845e+00 2.542693e+00 3004.9623 0.9999533
## spread[113] 1.867545e+00 2.469441e+00 2852.9102 0.9994708
## spread[114] 2.101288e+00 3.354226e+00 637.1554 0.9997870
## spread[115] 1.793384e+00 2.374124e+00 2502.1728 0.9992525
## spread[116] 1.716652e+00 2.277445e+00 2651.1052 1.0004758
## spread[117] 1.968968e+00 2.654410e+00 1684.6062 1.0040407
## spread[118] 2.059027e+00 3.210128e+00 1046.3790 1.0068669
## spread[119] 1.906029e+00 2.463406e+00 2798.0623 0.9996273
## spread[120] 2.145094e+00 2.807829e+00 1290.2593 1.0007344
## spread[121] 1.906134e+00 2.487856e+00 2718.3708 1.0007434
## spread[122] 1.507407e+00 1.949011e+00 3367.9209 1.0007484
## spread[123] 1.718148e+00 2.222491e+00 2482.1738 0.9996612
## spread[124] 2.002197e+00 2.578404e+00 2160.3542 1.0000877
## spread[125] 1.772665e+00 2.295941e+00 2505.8205 0.9996161
## spread[126] 2.071765e+00 2.910143e+00 1046.8661 1.0018889
## spread[127] 2.229066e+00 2.933777e+00 1096.5542 1.0017725
## spread[128] 1.811528e+00 2.699480e+00 720.6177 1.0035855
## spread[129] 1.547669e+00 2.051532e+00 2191.5911 0.9992870
## spread[130] 2.087061e+00 2.683448e+00 1298.5338 1.0052440
## spread[131] 1.538718e+00 2.004647e+00 2450.2075 0.9994543
## spread[132] 2.428947e+00 3.696448e+00 787.7916 1.0084238
## spread[133] 1.877512e+00 2.538874e+00 3184.5503 0.9993704
## spread[134] 1.979071e+00 2.534487e+00 2035.2196 0.9995148
## spread[135] 2.133282e+00 3.109111e+00 2108.9265 0.9998098
## spread[136] 2.285736e+00 2.929150e+00 1021.5009 1.0014028
## spread[137] 1.618213e+00 2.101966e+00 3147.5155 1.0003672
## spread[138] 1.721884e+00 2.202254e+00 2477.4604 0.9992743
## spread[139] 1.991691e+00 2.548507e+00 1039.3299 1.0008869
## spread[140] 1.599578e+00 2.070714e+00 3472.7173 0.9994940
## spread[141] 2.389982e+00 3.196683e+00 1936.8624 1.0001537
## spread[142] 1.821796e+00 2.635222e+00 1417.0526 0.9995378
## spread[143] 1.675681e+00 2.185850e+00 2681.1851 0.9999541
## spread[144] 2.192116e+00 2.871361e+00 2300.5034 1.0002249
## spread[145] 2.391440e+00 3.532803e+00 667.9968 1.0075889
## spread[146] 1.990854e+00 2.907962e+00 946.1955 1.0006642
## spread[147] 1.488356e+00 2.030472e+00 1188.4441 1.0020020
## spread[148] 2.012757e+00 2.968069e+00 1250.9286 1.0004145
## spread[149] 1.581874e+00 2.015731e+00 2598.1468 0.9992486
## spread[150] 1.636741e+00 2.136265e+00 2317.3695 0.9997099
## lapse[1] 1.306733e-01 1.829313e-01 1336.9670 1.0000008
## lapse[2] 2.597972e-02 7.365492e-02 1789.4989 0.9998359
## lapse[3] 2.725629e-02 6.484364e-02 2410.5355 1.0005639
## lapse[4] 1.900084e-02 6.450618e-02 1627.4720 1.0001495
## lapse[5] 4.394883e-02 9.065681e-02 1576.1615 1.0010099
## lapse[6] 8.413888e-03 3.202587e-02 2109.6577 0.9996194
## lapse[7] 2.022813e-02 6.467083e-02 1943.0725 0.9991563
## lapse[8] 6.765096e-02 1.191118e-01 851.4266 1.0076521
## lapse[9] 8.086989e-03 2.878117e-02 2357.1961 0.9993980
## lapse[10] 7.156767e-02 1.210161e-01 755.9048 1.0005435
## lapse[11] 3.318444e-02 7.637457e-02 2250.6211 0.9993979
## lapse[12] 1.186142e-02 3.963372e-02 2444.9713 0.9998622
## lapse[13] 8.070929e-03 2.937554e-02 2657.0686 1.0000792
## lapse[14] 2.026606e-01 2.590585e-01 2260.1528 0.9995327
## lapse[15] 4.904380e-02 1.098295e-01 1108.7386 1.0033297
## lapse[16] 9.427218e-03 3.187649e-02 2790.6002 0.9996718
## lapse[17] 1.657200e-02 4.643353e-02 2024.1190 1.0008459
## lapse[18] 8.585532e-03 2.904048e-02 2303.6803 1.0004851
## lapse[19] 3.348241e-01 3.937101e-01 2333.6067 0.9993624
## lapse[20] 1.095499e-02 4.041538e-02 1910.8133 0.9991397
## lapse[21] 1.886410e-02 6.574493e-02 1958.2315 1.0004737
## lapse[22] 9.696101e-03 3.419960e-02 2155.4698 1.0005924
## lapse[23] 1.902579e-02 6.054842e-02 2178.4552 0.9994775
## lapse[24] 4.101154e-01 4.684987e-01 2115.0178 0.9996026
## lapse[25] 5.252185e-02 1.075015e-01 1638.3416 1.0013636
## lapse[26] 6.547302e-02 1.166194e-01 1306.2463 0.9996846
## lapse[27] 9.485821e-03 3.392281e-02 2575.1381 0.9992911
## lapse[28] 2.528469e-02 7.119885e-02 1733.0123 1.0001266
## lapse[29] 1.238182e-02 4.965500e-02 1871.3700 0.9993275
## lapse[30] 1.211008e-01 1.777747e-01 644.2350 1.0022372
## lapse[31] 8.529003e-03 3.241058e-02 2083.4326 0.9999407
## lapse[32] 1.297305e-01 1.866207e-01 1360.6846 1.0009567
## lapse[33] 1.272136e-02 4.443849e-02 2600.3208 0.9995981
## lapse[34] 1.454504e-02 4.701149e-02 2585.1064 0.9991804
## lapse[35] 1.351231e-02 4.589627e-02 2320.6478 0.9995442
## lapse[36] 9.395520e-03 3.718692e-02 2467.7871 0.9991716
## lapse[37] 1.515682e-01 2.109238e-01 1541.5763 1.0001830
## lapse[38] 1.336594e-02 4.530045e-02 2964.6594 0.9991288
## lapse[39] 1.359106e-02 4.234216e-02 2119.3634 0.9999557
## lapse[40] 7.338186e-03 2.618109e-02 2696.2988 0.9997053
## lapse[41] 2.691935e-02 6.577189e-02 1780.6803 1.0011045
## lapse[42] 2.371388e-01 2.966877e-01 2846.0682 0.9997927
## lapse[43] 6.381972e-02 1.172359e-01 1453.3096 0.9997503
## lapse[44] 9.592900e-03 4.011907e-02 2370.8166 0.9990692
## lapse[45] 1.162701e-02 3.909942e-02 1963.7346 0.9993605
## lapse[46] 3.903824e-01 4.526265e-01 1827.6823 0.9990971
## lapse[47] 7.953277e-03 2.777476e-02 1944.3800 1.0002088
## lapse[48] 8.782371e-03 3.406692e-02 2407.1764 1.0009395
## lapse[49] 8.001736e-03 3.229472e-02 1689.8887 1.0010547
## lapse[50] 2.310614e-01 2.871781e-01 2360.2582 1.0030306
## lapse[51] 2.735119e-02 7.389757e-02 1697.3317 1.0025351
## lapse[52] 2.260739e-02 6.663573e-02 1821.6087 0.9995603
## lapse[53] 1.224468e-02 3.966896e-02 2594.6054 0.9997614
## lapse[54] 1.542648e-02 4.888922e-02 2192.7981 1.0012820
## lapse[55] 1.103492e-02 3.931568e-02 1915.0265 1.0021659
## lapse[56] 7.617517e-03 2.500689e-02 2416.8661 1.0003895
## lapse[57] 8.737833e-03 3.261477e-02 2385.7167 1.0000202
## lapse[58] 1.139664e-02 4.152090e-02 1968.6743 0.9993593
## lapse[59] 2.090250e-02 6.703767e-02 1924.7120 0.9994392
## lapse[60] 5.232029e-02 1.062564e-01 1556.1429 1.0000069
## lapse[61] 1.550560e-02 5.866156e-02 2347.9306 1.0003352
## lapse[62] 2.907914e-02 6.673367e-02 2376.6743 1.0002002
## lapse[63] 3.083239e-02 8.304891e-02 1580.8590 1.0004604
## lapse[64] 4.204405e-02 1.002478e-01 1602.7591 1.0014524
## lapse[65] 1.126542e-02 4.570297e-02 2059.6829 1.0004150
## lapse[66] 2.913593e-02 7.920719e-02 1733.9672 1.0010125
## lapse[67] 7.866089e-03 3.142476e-02 1935.7278 0.9993167
## lapse[68] 6.943417e-02 1.178143e-01 1201.8538 1.0003621
## lapse[69] 6.580680e-03 2.361638e-02 2208.9556 1.0003928
## lapse[70] 1.246323e-02 4.283114e-02 2396.1376 1.0000020
## lapse[71] 3.545404e-02 8.407553e-02 1643.6045 1.0026159
## lapse[72] 2.257772e-01 2.872763e-01 2179.6557 1.0000056
## lapse[73] 3.098259e-02 7.129652e-02 2014.5427 1.0031994
## lapse[74] 1.023450e-02 3.600629e-02 2220.9631 0.9992715
## lapse[75] 1.157068e-02 4.662276e-02 2223.0429 0.9994408
## lapse[76] 3.500680e-02 7.714779e-02 1745.2992 0.9994818
## lapse[77] 6.078820e-03 2.073885e-02 2411.5873 1.0005235
## lapse[78] 8.880078e-03 3.191242e-02 2265.5458 1.0004752
## lapse[79] 1.374942e-02 4.137048e-02 2555.1262 0.9992591
## lapse[80] 4.789763e-02 9.680647e-02 1820.5480 1.0005952
## lapse[81] 2.544054e-02 6.249568e-02 2868.6139 1.0007040
## lapse[82] 2.078648e-02 6.491193e-02 2024.2861 0.9995666
## lapse[83] 9.476246e-03 3.145906e-02 1940.2226 0.9994865
## lapse[84] 8.599853e-03 3.075256e-02 2544.1248 0.9993332
## lapse[85] 6.783485e-03 2.482402e-02 2643.5282 1.0002263
## lapse[86] 1.076400e-01 1.668412e-01 1346.3506 0.9991471
## lapse[87] 1.010301e-01 1.551526e-01 773.9607 1.0033575
## lapse[88] 1.725983e-02 5.625906e-02 2012.5978 1.0004885
## lapse[89] 5.398707e-02 1.027882e-01 1694.0654 0.9990752
## lapse[90] 3.610571e-02 9.081934e-02 1252.6438 1.0001068
## lapse[91] 7.878511e-03 3.063342e-02 2369.1191 1.0003887
## lapse[92] 2.136021e-02 6.125456e-02 1913.7871 1.0000428
## lapse[93] 6.701870e-02 1.181408e-01 1263.5239 0.9992312
## lapse[94] 2.332105e-01 2.875086e-01 2178.8437 0.9995868
## lapse[95] 1.076687e-02 4.291524e-02 2019.2540 1.0001652
## lapse[96] 1.093419e-01 1.563881e-01 803.1449 1.0015874
## lapse[97] 3.340653e-01 3.970719e-01 2339.7456 1.0002448
## lapse[98] 8.579994e-03 3.302224e-02 1983.0569 1.0014202
## lapse[99] 2.457877e-02 7.311079e-02 1896.7274 0.9997830
## lapse[100] 1.234881e-02 4.467156e-02 2659.6550 0.9996572
## lapse[101] 6.186530e-02 1.207391e-01 1154.3834 1.0038768
## lapse[102] 8.781108e-03 3.605555e-02 2386.3703 1.0025265
## lapse[103] 2.319012e-01 2.876745e-01 2432.8923 1.0004136
## lapse[104] 1.474412e-02 4.613940e-02 2744.5548 0.9997869
## lapse[105] 1.481267e-02 5.055754e-02 2188.8855 0.9999175
## lapse[106] 4.169837e-02 8.958701e-02 1637.3010 0.9999462
## lapse[107] 2.519174e-02 8.466716e-02 1881.2092 1.0006961
## lapse[108] 1.351156e-02 4.411959e-02 2288.2028 1.0005629
## lapse[109] 9.514449e-03 3.867353e-02 2094.9450 0.9997213
## lapse[110] 1.512401e-01 2.086770e-01 816.3788 1.0013415
## lapse[111] 9.049904e-03 3.660203e-02 2188.7798 0.9994037
## lapse[112] 1.203926e-02 4.385493e-02 2391.7493 0.9990963
## lapse[113] 1.077365e-02 3.851109e-02 2471.1380 1.0016121
## lapse[114] 1.048115e-01 1.585819e-01 1043.1837 1.0007530
## lapse[115] 8.664524e-03 3.169345e-02 2228.1004 0.9999167
## lapse[116] 9.676606e-03 3.801433e-02 2038.6504 0.9998107
## lapse[117] 3.692002e-02 8.871113e-02 2666.2466 0.9999918
## lapse[118] 1.549300e-01 2.111683e-01 1629.2493 1.0015103
## lapse[119] 1.182059e-02 4.285832e-02 2483.8628 0.9990738
## lapse[120] 1.100653e-02 4.075206e-02 2184.6115 0.9996759
## lapse[121] 1.037410e-02 3.431290e-02 2321.4963 1.0003673
## lapse[122] 8.345601e-03 2.947357e-02 2052.1189 1.0003969
## lapse[123] 9.554876e-03 3.738375e-02 2066.4911 0.9991736
## lapse[124] 1.156116e-02 4.239183e-02 2159.4257 0.9992690
## lapse[125] 1.131485e-02 4.539440e-02 1803.0135 0.9991031
## lapse[126] 5.216009e-02 1.011517e-01 1545.9450 1.0003623
## lapse[127] 3.402383e-02 8.179496e-02 1858.5275 1.0021039
## lapse[128] 1.626392e-01 2.165842e-01 1590.9595 1.0006571
## lapse[129] 6.862606e-03 2.676027e-02 1704.7847 0.9993275
## lapse[130] 2.602126e-02 7.427420e-02 2227.4424 1.0011784
## lapse[131] 1.053272e-02 3.371309e-02 2607.0319 1.0010286
## lapse[132] 8.855351e-02 1.410589e-01 1124.6297 1.0040961
## lapse[133] 1.157867e-02 4.135387e-02 1994.7461 1.0001609
## lapse[134] 1.261194e-02 5.129086e-02 1765.4204 1.0018868
## lapse[135] 3.621481e-01 4.241578e-01 2260.0714 0.9991660
## lapse[136] 1.561599e-02 5.860605e-02 2022.6141 0.9991864
## lapse[137] 1.043554e-02 3.691503e-02 2840.8225 1.0003822
## lapse[138] 1.129318e-02 4.202772e-02 2149.6459 1.0001958
## lapse[139] 1.472484e-02 5.206409e-02 1745.3948 0.9996027
## lapse[140] 7.854653e-03 3.201372e-02 2170.0469 1.0006414
## lapse[141] 2.588718e-02 7.963258e-02 1877.3937 0.9997856
## lapse[142] 5.890168e-02 1.007376e-01 1735.7335 0.9996071
## lapse[143] 9.008318e-03 3.241437e-02 2351.9247 1.0007868
## lapse[144] 2.927654e-02 7.886734e-02 2507.7714 1.0005562
## lapse[145] 8.445135e-02 1.357798e-01 1161.1911 1.0057818
## lapse[146] 4.593606e-02 9.322727e-02 1674.3422 1.0004514
## lapse[147] 7.740642e-03 2.727839e-02 2529.6627 0.9994264
## lapse[148] 6.222816e-02 1.152879e-01 2042.1526 1.0000591
## lapse[149] 9.361445e-03 3.521017e-02 2513.4999 0.9997966
## lapse[150] 8.591128e-03 3.100890e-02 2066.6446 0.9996821
## lp__ -6.474674e+03 -6.451897e+03 562.8472 1.0001156Results
Let’s take a look at our parameter estimates. Here’s the standard way to do this
plot(mdl,pars=c('b_threshold[1]','b_spread[1]','b_lapse[1]','b_threshold[2]','b_spread[2]','b_lapse[2]','b_threshold[3]','b_spread[3]','b_lapse[3]','sigma_log_threshold','sigma_log_spread','sigma_logit_lapse','threshold[1]','spread[1]','lapse[1]'))## ci_level: 0.8 (80% intervals)## outer_level: 0.95 (95% intervals)
There are some problems with this view. The parameter names for the condition means are indices into the vectors b_threshold, b_spread, and b_lapse, so these parameters are hard to interpret. Further, these hyperparameters for effects of visualization condition on the mean of each PF parameter are in a transformed parameter space. Their raw values are not very meaningful. What we need to do is recover meaningful parameter names and plug posterior samples into our model to generate possible estimated psychometric functions.
PFs for individuals
Getting the posterior
First, we need to recover our condition names from the numeric indices in our model. Thankfully, tidybayes will do this for us.
mdl %<>% recover_types(useData)Next, we’ll want to pull our posterior samples of individual PF parameter estimates into a tidy (i.e., long) data table.
# assign posterior samples to tidy tibble
post <- mdl %>% # should reduce to used params only
spread_draws(threshold[subject],spread[subject],lapse[subject])
# print table
post## # A tibble: 300,000 x 7
## # Groups: subject [150]
## .chain .iteration .draw subject threshold spread lapse
## <int> <int> <int> <fct> <dbl> <dbl> <dbl>
## 1 1 1 1 1 2.46 1.58 0.154
## 2 1 1 1 2 2.48 1.46 0.0354
## 3 1 1 1 3 2.39 1.25 0.0246
## 4 1 1 1 4 2.38 2.06 0.0107
## 5 1 1 1 5 2.43 1.98 0.0128
## 6 1 1 1 6 2.37 1.20 0.00136
## 7 1 1 1 7 2.26 1.34 0.0152
## 8 1 1 1 8 2.16 1.62 0.0571
## 9 1 1 1 9 2.58 1.38 0.000365
## 10 1 1 1 10 2.43 1.49 0.0635
## # ... with 299,990 more rowsSubset the posterior
Let’s look at only 100 (approximatedly equally likely) draws from our posterior, just to keep the amount of data we are processing and visualizing reasonable.
post_small =
post %>%
filter(.draw %in% floor(seq(1, 2000, length.out = 100)))Make a prediction grid
We’ll want to plot PFs for each subject across the range of intensity values observed. Since we can only plot so many subjects simultaneously in one view, we’ll make predictions for only a subset of subjects in this illustration.
n_intensity <- 101
intensity <- seq_range(useData$intensity, n = n_intensity)
grid = useData %>%
data_grid(nesting(condition, subject)) %>%
filter(as.numeric(subject) %in% 1:27) %>%
mutate(intensity = list(intensity))
grid## # A tibble: 27 x 3
## condition subject intensity
## <fct> <fct> <list>
## 1 c 1 <dbl [101]>
## 2 c 9 <dbl [101]>
## 3 c 13 <dbl [101]>
## 4 c 18 <dbl [101]>
## 5 c 19 <dbl [101]>
## 6 c 20 <dbl [101]>
## 7 c 24 <dbl [101]>
## 8 c 25 <dbl [101]>
## 9 c 27 <dbl [101]>
## 10 h 2 <dbl [101]>
## # ... with 17 more rowsRun the psychometric function over the prediction grid
Here, we call the psychometric function we defined above for each subject * draw from our posterior.
pfdf = grid %>%
inner_join(post_small) %>%
mutate(pf = pmap(list(intensity, threshold, spread, lapse), ~ psychometric(..1, ..2, ..3, 0.5, ..4))) %>%
unnest()## Joining, by = "subject"Plot the PF
Here, we create hypothetical outcome plots showing estimated psychometric functions for each draw from our posterior distribution of parameter estimates.
p = pfdf %>%
group_by(condition) %>%
mutate(subject = as.numeric(factor(subject))) %>%
filter(subject %in% 1:3) %>%
ggplot(aes(intensity, pf)) +
theme_minimal() +
geom_line() +
facet_grid(subject ~ condition, scales = "free") +
transition_manual(.draw)
animate(p, fps=2.5, width=500, height=300)
PFs for average individual in each condition
Getting the posterior
Next, we’ll want to pull our posterior samples of the population mean PF parameters into a tidy (i.e., long) data table.
# assign posterior samples to tidy tibble
post_avg <- mdl %>% # should reduce to used params only
spread_draws(b_threshold[condition],b_spread[condition],b_lapse[condition])
# print table
post_avg## # A tibble: 6,000 x 7
## # Groups: condition [3]
## .chain .iteration .draw condition b_threshold b_spread b_lapse
## <int> <int> <int> <fct> <dbl> <dbl> <dbl>
## 1 1 1 1 c 0.954 0.427 -3.97
## 2 1 1 1 h 0.880 0.456 -4.31
## 3 1 1 1 hf 0.803 0.526 -4.96
## 4 1 2 2 c 0.992 0.482 -4.03
## 5 1 2 2 h 0.874 0.393 -4.32
## 6 1 2 2 hf 0.820 0.594 -4.61
## 7 1 3 3 c 0.862 0.508 -4.12
## 8 1 3 3 h 0.797 0.506 -4.67
## 9 1 3 3 hf 0.927 0.615 -3.86
## 10 1 4 4 c 0.834 0.504 -4.33
## # ... with 5,990 more rowsSubset the posterior
Let’s look at only 100 (approximatedly equally likely) draws from our posterior, just to keep the amount of data we are processing and visualizing reasonable.
post_small_avg =
post_avg %>%
filter(.draw %in% floor(seq(1, 2000, length.out = 100)))Make a prediction grid
We’ll want to plot PFs across the range of intensity values observed. We’ll plot the average PF for each condition in our experiment.
n_intensity <- 101
intensity <- seq_range(useData$intensity, n = n_intensity)
grid = useData %>%
data_grid(condition) %>%
mutate(intensity = list(intensity))
grid## # A tibble: 3 x 2
## condition intensity
## <fct> <list>
## 1 c <dbl [101]>
## 2 h <dbl [101]>
## 3 hf <dbl [101]>Run the psychometric function over the prediction grid
Here, we call the psychometric function we defined above for each condition * draw from our posterior.
# this time we need to transform the parameters since these are our hyperparameters
pfdf_avg = grid %>%
inner_join(post_small_avg) %>%
mutate(pf = pmap(list(intensity, exp(b_threshold), exp(b_spread), plogis(b_lapse)), ~ psychometric(..1, ..2, ..3, 0.5, ..4))) %>%
unnest()## Joining, by = "condition"Plot the PF
Here, we create hypothetical outcome plots showing estimated psychometric functions for each draw from our posterior distribution of parameter estimates.
p = pfdf_avg %>%
group_by(condition) %>%
ggplot(aes(intensity, pf)) +
theme_minimal() +
geom_line() +
facet_grid(~ condition, scales = "free") +
transition_manual(.draw)
animate(p, fps=2.5, width=500, height=200)
Here’s the same plot using color rather than facting to differentiate conditions.
p = pfdf_avg %>%
group_by(condition) %>%
ggplot(aes(intensity, pf, color=condition)) +
theme_minimal() +
geom_line() +
transition_manual(.draw)
animate(p, fps=2.5, width=500, height=200)